Explanation Six types of inverse trigonometric functions are as follows: sin − 1 x , cos − 1 x , tan − 1 x , csc − 1 x , sec − 1 x , cot − 1 x . Domain of a function is the set of values where the function is defined. Range is the value for which the function would be defined. The respective domain and range are describes as shown: Function Domain Range sin − 1 x [ − 1 , 1 ] [ − π 2 , π 2 ] cos − 1 x [ − 1 , 1 ] [ 0 , π ] tan − 1 x ( −

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Find the exact value of an inverse trigonometric function.

Discuss the relationships among periodic functions, one-to- one functions, and inverse functions. With these relationships in mind, discuss what must happen for the trigonometric functions to have inverses.

2 Discussion In your own words, compare and contrast the reciprocal and inverse trigonometric functions. • What do the functions have in common? • Where do these functions differ? • In which situation(s) would you use a reciprocal function? • In which situation(s) would you use an inverse function? In your opinion, which type of function is most useful?

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Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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Chapter 1 Solutions