Multiple Choice
Evaluate the expression.
11. Inverse Trigonometric Functions and Basic Trig Equations
Inverse Sine, Cosine, & Tangent
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Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.
A
0.34
B
– 0.34
C
– 0.33
D
– 19.47
Verified step by step guidance1
Understand that \( \sin^{-1}(x) \) represents the inverse sine function, which gives the angle whose sine is \( x \).
Recognize that the input \( -\frac{1}{3} \) is within the valid range for the inverse sine function, which is \([-1, 1]\).
Use a calculator to find \( \sin^{-1}(-\frac{1}{3}) \). Ensure the calculator is set to radian mode, as the problem asks for the answer in radians.
The calculator will provide an angle in radians. Note that the range of \( \sin^{-1}(x) \) is \([-\frac{\pi}{2}, \frac{\pi}{2}]\), so the result will be a negative angle.
Round the result to two decimal places to match the problem's requirement.
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