객관식
What is the range of ?
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5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
객관식
Evaluate the expression.
A
B
C
D
검증된 단계별 안내1
Understand the problem: We need to evaluate the expression \( \sin^{-1}(1) \). This involves finding the angle whose sine is 1.
Recall the definition of \( \sin^{-1}(x) \): The inverse sine function, \( \sin^{-1}(x) \), returns the angle \( \theta \) such that \( \sin(\theta) = x \) and \( \theta \) is in the range \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
Identify the angle: The sine of \( \frac{\pi}{2} \) is 1, which means \( \sin^{-1}(1) = \frac{\pi}{2} \).
Verify the range: Ensure that \( \frac{\pi}{2} \) is within the range \([-\frac{\pi}{2}, \frac{\pi}{2}]\), which it is.
Conclude the evaluation: The expression \( \sin^{-1}(1) \) evaluates to \( \frac{\pi}{2} \).
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