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Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.
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11. Inverse Trigonometric Functions and Basic Trig Equations
Inverse Sine, Cosine, & Tangent
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Evaluate the expression.
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Understand that the expression involves the inverse sine function, \( \sin^{-1}(x) \), which gives the angle whose sine is \( x \).
Recognize that \( \sin^{-1}(1) \) asks for the angle whose sine value is 1.
Recall that the sine of \( \frac{\pi}{2} \) is 1, which is within the range of the inverse sine function \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
Conclude that \( \sin^{-1}(1) = \frac{\pi}{2} \) because \( \frac{\pi}{2} \) is the angle in the specified range that satisfies the condition.
Verify that the answer \( \frac{\pi}{2} \) is correct by considering the unit circle, where the sine of \( \frac{\pi}{2} \) is indeed 1.
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