Transcript CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Chapter 6 – Trigonometric Functions:
Right Triangle Approach
6.4 - Inverse Trigonometric Functions and Right
Triangles
Remember…

The inverse sine function is the function sin-1 with
domain [-1, 1] and range [- ⁄ 2,  ⁄ 2] defined by
1
sin x  y  sin y  x
6.4 - Inverse Trigonometric Functions and Right
Triangles
Remember…

The inverse cosine function is the function cos-1
with domain [-1, 1] and range [0, ] defined by
1
cos x  y  cos y  x
6.4 - Inverse Trigonometric Functions and Right
Triangles
Remember…

The inverse tangent function is the function tan-1
with domain (-∞, ∞) and range (- ⁄ 2,  ⁄ 2) defined
by
1
tan x  y  tan y  x
6.4 - Inverse Trigonometric Functions and Right
Triangles
Remember…
6.4 - Inverse Trigonometric Functions and Right
Triangles
Examples – pg. 467

Find the exact value of each expression, if it is
defined.
 1
5. (a) sin   
 2
1
(b) cos  
2
 3
(c) tan 

 3 
6. (a) sin 1  1
(b) cos 1 1
(c) tan 1  0 
1
1
6.4 - Inverse Trigonometric Functions and Right
Triangles
1
Examples – pg. 467

Use a calculator to find an approximate value of each
expression rounded to five decimal places, if it is
defined.
8. cos 1  0.75 
1
10. sin  
3
1
12. tan 1  4 
6.4 - Inverse Trigonometric Functions and Right
Triangles
Examples – pg. 467

Find the angle
in degrees, rounded to one decimal.
6.4 - Inverse Trigonometric Functions and Right
Triangles
Examples – pg. 467

Find all the angles between 0
satisfying the given equation.
3
22. sin  
2
and 180
1
26. cos  
9
6.4 - Inverse Trigonometric Functions and Right
Triangles
Evaluating Compositions
5.5 - Inverse Trigonometric Functions & Their
Graphs
Examples – pg. 468

Find the exact value of the expression.
 1 4 
28. tan  sin

5

 1 12 
29. sec  sin

13 

 1 7 
30. csc  cos

25


 1 12 
31. tan  sin

13


 1 2 
32. cot  sin

3

6.4 - Inverse Trigonometric Functions and Right
Triangles
Evaluating Compositions
Evaluate the following:
2

1. tan  arccos 
3

 1 5 
3. cos  tan

12 

7 

2. sin  cos

4 

 1 1 
4. cot  sin  
3

1
6.4 - Inverse Trigonometric Functions and Right
Triangles
Examples – pg. 468

Rewrite the expression as an algebraic expression in
x.




34. sin tan 1 x
36. cos tan 1 x

35. tan sin 1 x
6.4 - Inverse Trigonometric Functions and Right
Triangles

Calculus Problems Made Easy
Write the following as an algebraic expression in x.
a. sin  cos
1
b. cot  cos
1
 3x  
1
0 x
3
 3x  
1
0 x
3
6.4 - Inverse Trigonometric Functions and Right
Triangles
Example – pg. 468
6.4 - Inverse Trigonometric Functions and Right
Triangles