Inverse Trigonometric Ratios Worksheet
Explore inverse trigonometric ratios (arcsin, arccos, arctan) with this Grade 11 math worksheet, covering definitions, calculations, and applications.
Includes
Standards
Inverse Trigonometric Ratios
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. What is the range of the inverse sine function, arcsin(x)?
[0, π]
[-π/2, π/2]
(0, π)
(-π/2, π/2)
2. If cos(θ) = 0.5, what is the principal value of θ in radians?
π/6
π/4
π/3
π/2
3. The domain of the inverse tangent function, arctan(x), is .
4. To find an angle when you know its sine, you use the function.
5. Explain why the inverse trigonometric functions have restricted domains and ranges.
6. A ladder is leaning against a wall. If the ladder is 10 feet long and reaches 8 feet up the wall, what angle does the ladder make with the ground? Round your answer to one decimal place.
7. The expression arcsin(2) has a real solution.
True
False
8. arctan(x) can produce an angle greater than π/2 radians.
True
False
Match each inverse trigonometric function with its corresponding domain.
9. arcsin(x)
a. (-∞, ∞)
10. arccos(x)
b. [-1, 1]
11. arctan(x)
c. [-π/2, π/2]
12. Evaluate the following expressions without using a calculator:
a) arcsin(sin(π/4))
b) cos(arccos(-1/2))
c) tan(arctan(√3))