A Graphical Approach to Precalculus with Limits (7th Edition)

Chapter 10

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Use a graphing calculator to graph the given ... more

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; Use a graphing calculator to graph the given ... more

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Apply the relations between trigonometric ratios ... more

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; The cofunction of is  .The cofunction of is... more

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The new equation obtained in the previous question... more

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Use the relations between trigonometric ratios to ... more

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; The equation is .The cofunctions of , , and ... more

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Use relations between trigonometric ratios to ... more

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1 ; The Pythagorean identity in sine and cosine of... more

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; The Pythagorean identity in secant and tangent ... more

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; The Pythagorean identity in cosecant and ... more

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; The cosecant of any angle is the reciprocal of ... more

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; The secant of any angle is the reciprocal of ... more

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; The quotient of the sine and cosine of any ... more

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; The even-odd identity states that , where is ... more

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; The even-odd identity states that , where is ... more

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; The even-odd identity states that , where is ... more

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; The even-odd identity states that , where is ... more

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; The even-odd identity states that , where is ... more

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; The even-odd identity states that , where is ... more

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The quotient identity states that .The value of ... more

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The quotient identity states that .The even-odd ... more

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The individual neglects to note down the argument ... more

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The square root of is not equal to . ; The ... more

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; ; The Pythagorean identity in cosecant and ... more

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; ; ; The Pythagorean identity in sine and cosine ... more

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;;; ; The pythagorean identity states that .... more

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;; ; The pythagorean identity states that .... more

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;;; ; The pythagorean identity states that .Take ... more

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;;; ; The pythagorean identity states that .Take ... more

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; The quotient identity for the tangent of any ... more

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; The quotient identity for the cotangent of any ... more

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; The quotient identity for the tangent of any ... more

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; The quotient identity for the cotangent of any ... more

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; The Pythagorean identity in secant and tangent ... more

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; The Pythagorean identity in cosecant and ... more

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; The Pythagorean identity in secant and tangent ... more

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; The Pythagorean identity in cosecant and ... more

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; The quotient identity for the cotangent of any ... more

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1 ; The quotient identity for the cotangent of any... more

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; The cosecant function is the reciprocal of the ... more

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; The secant function is the reciprocal of the ... more

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; The cotangent function is the ratio of sine and... more

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; The tangent function is the ratio of sine and ... more

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; The Pythagorean identity in sine and cosine of ... more

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; The cotangent function is the ratio of cosine ... more

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; The secant function is the reciprocal of the ... more

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; The cotangent function is the reciprocal of the... more

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; Apply the Pythagorean identity in cosecant and ... more

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; Use the formula of , where and are real ... more

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; The FOIL principle of multiplication states ... more

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; Separate the denominator in the given ... more

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; Separate the denominator in the given ... more

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; Use the Pythagorean identity in and , i.e., , ... more

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; The secant function is the reciprocal of the ... more

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; Use the Pythagorean identity in and , i.e., , ... more

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; The distributive property of multiplication ... more

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; The FOIL principle of multiplication states ... more

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; The cosecant function is the reciprocal of the ... more

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; In the fourth quadrant, the cosine function is ... more

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. ; Rewrite the given expression with a common ... more

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; The secant function is the reciprocal of the ... more

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; The tangent function is the ratio of sine and ... more

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; The distributive property of multiplication ... more

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1 ; The cosecant of any angle is the reciprocal of... more

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; The LCM of denominators in the given expression... more

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1 ; The secant function is the reciprocal of .The ... more

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; Cross Multiply the denominator with first term ... more

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; Expand the square by using the formula i.e., .... more

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; Expand the square by using the formula i.e., .... more

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; The least common denominator of the given ... more

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; Use an identity , where and are real numbers... more

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Substitute for and for in the left hand side ... more

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Substitute for and for in the left hand side ... more

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Substitute for in the left hand side of the ... more

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Substitute for in the right hand side of the ... more

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Substitute for in the left hand side of the ... more

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Substitute for in the left hand side of the ... more

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Use the trigonometric identity in the numerator ... more

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Substitute for in the numerator of the left hand... more

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Substitute for and for in the right hand side ... more

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Substitute for in the left hand side of the ... more

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Substitute for in the left hand side of the ... more

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Write the numerator of the left hand side of the ... more

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Use an associative property of addition that is , ... more

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Substitute for and for in the left hand side ... more

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Substitute for in the numerator of the left hand... more

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Consider the left hand side of the given equation.... more

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Substitute for in the left hand side of the ... more

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Write the left hand side of the given equation in ... more

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Substitute for in the left hand side of the ... more

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Substitute for in the left hand side of the ... more

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Use an identity in the numerator of the left hand... more

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Multiply the numerator and denominator of the ... more

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Multiply the numerator and denominator of the ... more

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Substitute for , for and for in the left hand... more

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Factor out from the left hand side of the given ... more

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Use an identity , where , and are real numbers, ... more

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Write the numerator of the left hand side of the ... more

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Multiply the numerator and denominator of the ... more

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Substitute for in the right hand side of the ... more

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Multiply in the numerator and denominator of the ... more

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Substitute for and for in the left hand side ... more

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Multiply each term of the first factor by each ... more

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Multiply in the numerator and denominator of the ... more

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Multiply the numerator and denominator of the ... more

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Multiply the numerator and denominator of the ... more

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Multiply in the numerator and denominator of the ... more

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Use an identity and , where and are real ... more

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Use the distributive property of multiplication ... more

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Substitute for , for and for in the left hand... more

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Use an identity , where and are real numbers, in... more

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The cosine of the sum of two angles and , i.e... more

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; The sine of the difference of two angles, i.e... more

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; The tangent of the difference of two angles, i.... more

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; The tangent function is an odd function, ... more

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; The sine function is an odd function, i.e., . ... more

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; The sine of the sum of two angles, i.e., is ... more

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; The cosine of the sum of two angles, i.e., is ... more

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; The cosine of the sum of two angles, i.e., is ... more

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; The sine of the sum of two angles, i.e., is ... more

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; The tangent function of the sum of two angles ... more

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; The sine of the difference of two angles is ... more

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; The cosine of the difference of two angles is ... more

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; The tangent function is an odd function and ... more

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; The cosine of the sum of two angles is given ... more

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; The cosine of the difference of two angles is ... more

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; The sine of the difference of two angles is ... more

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1 ; The sine of the sum of two angles is given by... more

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; The tangent function of the sum of two angles ... more

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; The tangent function is an odd function and ... more

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; The sine of difference of two angles is given ... more

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; The sine of the sum of two angles is given by ... more

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; The cosine of the sum of two angles is given ... more

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; The cosine of the difference of two angles is ... more

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; The sine of difference of two angles is given ... more

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; The sine of the sum of two angles is given by ... more

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; The tangent function of difference of two ... more

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; The tangent function of the difference of two ... more

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; The cosine of difference of two angles is ... more

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; The difference formula for cosine is stated as... more

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; The sum formula for cosine is stated as .Use ... more

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; The difference formula for sine is stated as .... more

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; The sum formula for sine is stated as .Use the ... more

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; The difference formula for is stated as .Use ... more

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; The difference formula for cosine is stated as... more

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; The sum formula for sine is stated as .Use the ... more

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; The sum formula for is stated as .Use the sum ... more

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; The sum formula for is stated as .Use the sum ... more

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; The difference formula for is stated as .Use ... more

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; The difference formula for sine is stated as .... more

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; The difference formula for is stated as .Use ... more

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; The sum formula for is stated as .Use the sum ... more

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; The difference formula for cosine is stated as... more

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; The difference formula for cosine is stated as... more

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Substitute for in the identity . ; The identity ... more

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Write the term as the sum and as the sum in ... more

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Use the identities and to simplify the given ... more

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Use the identity to simplify the given expression... more

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Use the identity .Substitute for and for in ... more

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Use the identity .Substitute for and for in ... more

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Use the identity and the identity .Substitute 1 ... more

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Use the identity .  ; The identity for tangent ... more

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Use the identity and the identity .  Substitute ... more

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Use the identity and the identity . Substitute ... more

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3 ; A sine or cosine graph completes one cycle in ... more

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163; ; No ; The voltage of the alternating current... more

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; The reciprocal identity for is .The quotient ... more

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; The sine difference identity is .Apply the sine... more

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, , ; Substitute for in the equation to obtain ... more

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Substitute for and substitute for in the left ... more

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Multiply and divide the left side of the given ... more

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Substitute for , for and for in the left hand... more

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Simplify the left-side of the given equation.The ... more

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; Use the identity to factor out as a common ... more

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The student should conclude from the graph that ... more

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Use the identity to write the given expression as... more

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Negative ; The half angle identity for is .... more

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Positive ; The half angle identity for is .... more

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Positive ; The half angle identity for is .... more

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Negative ; The half angle identity for is .... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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1 ; The double-angle identity corresponding to the... more

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; The double-angle identity corresponding to the ... more

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. ; Switch ON the graphing calculator.Press the ... more

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; Switch ON the graphing calculator.Press the ... more

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;The graph of is as shown in the graph below. ; ... more

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;The graph of is as shown in the graph below. ; ... more

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;The graph of is as shown in the graph below. ; ... more

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;The graph of is as shown in the graph below. ; ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The double-angle identity corresponding to the ... more

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; The tangent function of the sum of two angles ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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3 ; Use the trigonometric identity to evaluate ... more

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; Use the trigonometric identity to evaluate the... more

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; Use the trigonometric identity to evaluate the... more

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; Use the trigonometric identity to evaluate the... more

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; As is the reciprocal of , therefore .Use the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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; The half-angle identity corresponding to the ... more

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Substitute in the given expression by and ... more

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Substitute for and substitute for in the given ... more

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Since, secant function is the reciprocal of cosine... more

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The secant function is the reciprocal of the ... more

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Simplify the right-side of the given equation.The ... more

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Simplify the left-side of the given equation.The ... more

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Simplify the left side of the given equation.The ... more

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Simplify the right-side of the given equation.The ... more

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Simplify the right-side of the given equation.The ... more

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Simplify the left-side of the given equation.The ... more

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Express the tangent function in the given equation... more

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Express the cosecant, tangent and cotangent ... more

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Simplify the right hand side of the given equation... more

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Simplify the right side of the given expression.... more

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Solve the right-side of the given equation.The ... more

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Substitute for in the given expression and ... more

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; Use the identity to simplify the given ... more

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; Use the identity to simplify the given ... more

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; Use the identity to simplify the given ... more

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; Multiply the given expression by the unit ... more

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; Use the identity to simplify the given ... more

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; Use the identity to simplify the given ... more

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; Since sine is an odd function, is equal to .Use... more

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; Use the identity to simplify the given ... more

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; Use the identity to simplify the given ... more

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; Use the identity to simplify the given ... more

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Rewrite the terms on the left hand side of the ... more

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Use the identity on the left hand side of the ... more

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Multiply on the numerator and denominator of the ... more

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Rewrite the numerator of the expression on the ... more

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Square both sides of the trigonometric identity ... more

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Use the identity  in the numerator, substitute ... more

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Use the identity to rewrite the tangent function ... more

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Factorise the expression on the left hand side of ... more

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Add the two fractions on the left hand side of the... more

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Use the identity in the expression on the left ... more

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Use the identity to expand the expression on the ... more

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Use the identity on the left hand side of the ... more

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The half number identity for cosine function is .... more

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Factorise the expression on the left hand side of ... more

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Factor out the term from the numerator of the ... more

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Simplify the left side of the given equation using... more

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Simplify the left side of the given equation using... more

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Simplify the left side of the given equation using... more

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; Observe the given graph to determine the -... more

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; Observe the given graph to determine the -... more

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0 ; Observe the given graph to determine the -... more

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The angle 1.401592654 radian lies in the first ... more

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one-to-one ; A function is said to be one-to-one ... more

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range ; The domain of an inverse function is the ... more

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; In order to obtain the result, simply the ... more

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; ; The difference between an original function ... more

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; The domain of is the range of and the range ... more

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Switch all the and values in each point to graph... more

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; The value of the given expression is the number... more

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0 ; The value of the given expression is the ... more

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; The range of the function or is defined for .... more

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does not exist ; The number in the expression ... more

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does not exist ; The number in the equation is ... more

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does not exist. ; The number in the expression ... more

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does not exist. ; The number in the expression ... more

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; Turn on the graphing calculator.Press the MODE ... more

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; Turn on the graphing calculator.Press the MODE ... more

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; The term is the same as .Turn on the graphing ... more

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; The term is the same as .Turn on the graphing ... more

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; The term is equivalent to .Turn on the ... more

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; The term is equivalent to .Turn on the ... more

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0.83798122 ; Turn on the graphing calculator.Press... more

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0.9601269848 ; Turn on the graphing calculator.... more

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2.3154725 ; The term is equivalent to .Turn on ... more

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2.460522109 ; The term is equivalent to .Turn on ... more

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1.190023793 ; Turn on the graphing calculator.... more

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1.108230308 ; Turn on the graphing calculator.... more

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Substitute arbitrary values for from the interval... more

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The domain of the inverse sine function is . The ... more

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The value 1.003 belongs to the domain of the ... more

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; Consider as .Equate for i.e. . It implies ... more

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; Consider as .Equate for i.e.  .It implies ... more

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; The value of is .Substitute for in the given... more

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; Consider as .Equate to i.e.  . It implies ... more

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; The term can be written as . The value of is ... more

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; The term can be written as . The value of is ... more

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5 ; Consider . Thus, , i.e. .The value of is ... more

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; Consider , therefore , i.e. .The value of is ... more

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2 ; Consider , therefore , i.e. .The value of is ... more

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3 ; Consider , therefore , i.e. .The value of is ... more

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; The angle is in the second quadrant and the ... more

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; The angle is in the second quadrant and the ... more

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; Consider . Therefore, .The value of is ... more

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0.894427191 ; Turn on the calculator.Press the ... more

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0.9682458366 ; Turn on the calculator.Press the ... more

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0.123499811 ; Turn on the calculator.Press the ... more

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0.716386406 ; Turn on the calculator.Press the ... more

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; Consider the diagram, where point O is the ... more

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Consider the height of the taller building as ... more

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; The figure shows the cross section of the oil ... more

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; The half-angle identity corresponding to the ... more

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;; ; The trigonometric identity involving sine and... more

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; The identity corresponding to the sine function... more

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; The product-to-sum identity corresponding to ... more

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The inverse cosecant function is a decreasing ... more

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; The function is the inverse cotangent function... more

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; From the given graph, determine the intervals ... more

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; Subtract 1 from both sides of the given ... more

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; Subtract 1 from both sides of the given ... more

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; Add 6 on both sides of the given equation.... more

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; Subtract 5 from both sides of the given ... more

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; Subtract 3 from both sides of the given ... more

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; Subtract and 4 from both sides of the given ... more

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; Subtract and 1 from both sides of the given ... more

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; The zero product property states that if , ... more

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; The zero product property states that if , ... more

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; Subtract from both sides of the equation.... more

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