Rogers Olson
05/02/2024 · Primary School
Evaluate the following expressions. Your answer must be an angle in radians and in the interval \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) (a) \( \sin ^{-1}(1)=\square \) (b) \( \sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)=\square \) (c) \( \sin ^{-1}\left(-\frac{1}{2}\right)=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \arcsin(1) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arcsin\left(1\right)\)
- step1: Calculate the trigonometric value:
\(\frac{\pi }{2}\)
Calculate or simplify the expression \( \arcsin(-\sqrt(2)/2) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arcsin\left(-\frac{\sqrt{2}}{2}\right)\)
- step1: Rewrite the expression:
\(-\arcsin\left(\frac{\sqrt{2}}{2}\right)\)
- step2: Calculate:
\(-\frac{\pi }{4}\)
Calculate or simplify the expression \( \arcsin(-1/2) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arcsin\left(\frac{-1}{2}\right)\)
- step1: Rewrite the fraction:
\(\arcsin\left(-\frac{1}{2}\right)\)
- step2: Rewrite the expression:
\(-\arcsin\left(\frac{1}{2}\right)\)
- step3: Calculate:
\(-\frac{\pi }{6}\)
The evaluated expressions are as follows:
(a) \( \sin^{-1}(1) = \frac{\pi}{2} \)
(b) \( \sin^{-1}\left(-\frac{\sqrt{2}}{2}\right) = -\frac{\pi}{4} \)
(c) \( \sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6} \)
Quick Answer
(a) \( \sin^{-1}(1) = \frac{\pi}{2} \)
(b) \( \sin^{-1}\left(-\frac{\sqrt{2}}{2}\right) = -\frac{\pi}{4} \)
(c) \( \sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6} \)
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