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```NAME
DATE
4-6
PERIOD
Practice
Inverse Trigonometric Functions
Sketch the graph of each function.
1. y = arccos 3x
2. y = arctan x + 1
y
π
π
π
2
y
π
2
1x
0.5
-1 -0.5 0
-2 -1
-π
2
-π
-π
4. y = tan −1 3x
3. y = sin −1 3x
π
2x
1
0
-π
2
y
π
y
π
2
π
2
-1 -0.5 0
1x
0.5
-2 -1
-π
2
-π
-π
2x
1
0
-π
2
Find the exact value of each expression, if it exists.
√3
2
)
(
3π
7. tan − −
2
(
)
π
−−
√3
3
)
3
2)
π
8. sin −1 cos −
)
π
−
3
3
√3
3
−
3
6
1
10. arcsin − −
π
-−
(
√3
3
( 2)
6
(
π
−
(
π
−−
1
11. tan sin -1 1 - cos -1 −
)
(
undefined
9. arctan - −
π
6. cos −1 cos −
6
)
12. sin arctan − −
1
−−
2
13. ART Hans purchased a painting that is 30 inches tall that will hang 8 inches
above the fireplace. The top of the fireplace is 55 inches from the floor.
a. Write a function modeling the maximum viewing angle θ for the distance d
for Hans if his eye-level when sitting is 2.5 feet above the ground.
(d)
(d)
63
33
θ = tan −1 −
− tan −1 −
b. Determine the distance that corresponds to the maximum viewing angle. 46.6 in.
Write each trigonometric expression as an algebraic expression of x.
14. sin (arccos x)
Chapter 4
√
1 - x2
x √
1 - x2
1-x
15. tan (sin −1 x) −
2
34
Glencoe Precalculus