Explanation Given the figure below: Now, we already have that ( cos π 2 , sin π 2 ) = ( 0 , 1 ) ( cos 2 π 3 , sin 2 π 3 ) = ( − 1 2 , 3 2 ) ( cos 3 π 4 , sin 3 π 4 ) = ( − 2 2 , 2 2 ) ( cos 5 π 6 , sin 5 π 6 ) = ( − 3 2 , 1 2 ) ( cos π , sin π ) = ( 1 , 0 ) Now, the point on the unit circle that corresponds to the angle θ = 7 π 6 lies opposite to the point with angle π 6 . Thus, ( cos 7 π 6 , sin 7 π 6 ) = ( − cos π 6 , − sin π 6 ) = ( − 3 2 , − 1 2 ) Now, the point on the unit circle that corresponds to the angle θ = 5 π 4 lies opposite to the point with angle π 4 . Thus, ( cos 5 π 4 , sin 5 π 4 ) = ( − cos π 4 , − sin π 4 ) = ( − 2 2 , − 2 2 ) Now, the point on the unit circle that corresponds to the angle θ = 4 π 3 lies opposite to the point with angle π 3 . Thus, ( cos 4 π 3 , sin 4 π 3 ) = ( − cos π 3 , − sin π 3 ) = ( − 1 2 , − 3 2 ) Now, the point on the unit circle that corresponds to the angle θ = 3 π 2 lies opposite to the point with angle π 2 . Thus, Now, the point on the unit circle that corresponds to the angle θ = 5 π 3 lies opposite to the point with angle 2 π 3 . Thus, ( cos 5 π 3 , sin 5 π 3 ) = ( − cos 2 π 3 , − sin 2 π 3 ) = ( 1 2 , − 3 2 ) Now, the point on the unit circle that corresponds to the angle θ = 7 π 4 lies opposite to the point with angle 3 π 4

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 1.4, Problem 7E

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Values of (cosθ,sinθ) for the points in the figure below:

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Chapter 1.4, Problem 6E

Chapter 1.4, Problem 8E

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

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Chapter 1 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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