6.4 - Inverse Trigonometric Functions and Right Triangles

Section 6.4 Inverse

Trigonometric Functions &

Right Triangles

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

1sin sinx y 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

1cos cosx y 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 1tan tanx y y x

6.4 - Inverse Trigonometric Functions and Right Triangles

Remember…

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 467Find the exact value of each expression, if it is

defined.

1 1 1

1 1 1

1 1 35. (a) sin (b) cos (c) tan

2 2 3

6. (a) sin 1 (b) cos 1 (c) tan 0

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 467Use a calculator to find an approximate value of each

expression rounded to five decimal places, if it is defined.

1

1

1

8. cos 0.75

110. sin

3

12. tan 4

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 467Find the angle in degrees, rounded to one decimal.

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 467Find all the angles between 0 and 180 satisfying

the given equation.

3 122. sin 26. cos

2 9

5.5 - Inverse Trigonometric Functions & Their Graphs

Evaluating Compositions

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 468Find the exact value of the expression.

1 1

1 1

1

4 1228. tan sin 29. sec sin

5 13

7 1230. csc cos 31. tan sin

25 13

232. cot sin

3

6.4 - Inverse Trigonometric Functions and Right Triangles

Evaluating Compositions

Evaluate the following:

1

21. tan arccos

3

72. sin cos

4

1

1

53. cos tan

12

14. cot sin

3

6.4 - Inverse Trigonometric Functions and Right Triangles

Examples – pg. 468Rewrite the expression as an algebraic expression in x.

1 1

1

34. sin tan 35. tan sin

36. cos tan

x x

x

6.4 - Inverse Trigonometric Functions and Right Triangles

Calculus Problems Made EasyWrite the following as an algebraic expression in x.

1

1

1a. sin cos 3 0

3

1b. cot cos 3 0

3

x x

x x

6.4 - Inverse Trigonometric Functions and Right Triangles

Example – pg. 468