객관식
Evaluate the expression.
455
views
8
rank
11. Inverse Trigonometric Functions and Basic Trig Equations
Inverse Sine, Cosine, & Tangent
객관식
Evaluate the expression.
A
B
C
D
검증된 단계별 안내1
Understand that the expression \( \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) \) asks for the angle whose sine is \( \frac{\sqrt{2}}{2} \).
Recall that the sine of \( \frac{\pi}{4} \) is \( \frac{\sqrt{2}}{2} \). Therefore, \( \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4} \).
Consider the range of the inverse sine function, which is \([-\frac{\pi}{2}, \frac{\pi}{2}]\). This means the principal value of \( \sin^{-1} \) will be within this interval.
Verify that \( \frac{\pi}{4} \) is within the range of \([-\frac{\pi}{2}, \frac{\pi}{2}]\), confirming it as a valid solution.
Conclude that the correct angle corresponding to \( \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) \) is \( \frac{\pi}{4} \).
관련 영상
관련 실천
