1. Sullivan Algebra and Trigonometry: Section 7.1 The Inverse Sine, Cosine, and Tangent Functions Objectives of this Section Find the Exact Value of the Inverse Sine, Cosine, and Tangent Functions Find the Approximate Value of the Inverse Sine, Cosine, and Tangent Functions

2. Let f denote a one-to-one function y = f (x). The inverse of f, denoted f -1, is a function such that f -1 (f (x)) = x for every x in the domain f and f (f -1 (x)) = x for every x in the domain of f -1. In other words, the function f maps each x in its domain to a unique y in its range. The inverse function f -1 maps each y in the range back to the x in the domain. Recall the Definition of the Inverse Function

3. To find the inverse of the sine function, first examine the graph to see if the function is one - to - one, using the horizontal line test. y = b -1< b < 1

4. Since the sine function is not one - to - one for all real numbers, we must restrict the domain to an interval where the function is one - to - one. x y 1

5. The inverse sine of x

10. To find the inverse of the cosine function, first examine the graph to see if the function is one - to - one, using the horizontal line test. y = b -1 < y < 1

11. Since the cosine function is not one - to - one for all real numbers, we must restrict the domain to an interval where the function is one - to - one.

12. The inverse cosine of x

17. To find the inverse of the tangent function, first examine the graph to see if the function is one - to - one, using the horizontal line test.

18. Since the tangent function is not one - to - one for all real numbers, we must restrict the domain to an interval where the function is one - to - one.

19. The inverse tangent of x