1. 1 Lecture 7 of 12 Inverse Trigonometric Functions

2. 2 Learning Outcomes Define the inverse of trigonometric functions. Sketch the graphs of trigonometric functions and their inverse.

3. 3 Inverse Trigonometric Functions Inverse function is valid if the function is one-to-one function sin-1 (x), cos-1 (x) and tan-1 (x) can be defined for a restricted domain. These domain are the values of x for which the sine, cosine and tangent mappings are one-to-one.

4. 4 For f(x) = sin(x) to be one-to-one mappings, For f(x) = sin(x) to be one-to-one mappings, For f(x) = cos(x) to be one-to-one mapping, D f = [ 0,  ] For f(x) = tan(x) to be one-to-one mappings,

5. 5 Graph of y = sin-1(x), y = cos-1(x) and y = tan-1(x) can be sketch by reflecting the graphs of y = sin(x), y = cos(x) and y = tan(x) in the line of y = x.

6. 6 Graph y = sin -1 (x) Domain : [ -1, 1 ] Domain : [ -1, 1 ] Range : Range :

7. 7 Graph y = cos -1 (x) Domain : [ -1, 1 ] Domain : [ -1, 1 ] Range : [ 0,  ] Range : [ 0,  ]

8. 8 y = tan -1 (x) y = tan (x)

9. 9 Graph y = tan -1 (x) Domain : Range : Asymptote :

10. 10 Example 1 Find the exact value of each expression if it is defined. Find the exact value of each expression if it is defined.

11. 11 Solution = 6

12. 12 Example 2 Find the value without using calculator

13. 13 Solution (a)Let y = sin -1 sin y = Since

14. 14 (b)Let y = cos -1 cos y = Since

15. CONCLUSION 15 Inverse function is valid if the function is one-to-one function sin-1 (x), cos-1 (x) and tan-1 (x) can be defined for a restricted domain. These domain are the values of x for which the sine, cosine and tangent mappings are one-to-one.