Download presentation
Presentation is loading. Please wait.
Published byChad Aubrey Ward Modified over 8 years ago
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.
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.