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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