Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
-$\sin \left( \cos ^ { - 1 } 0.8324 \right)$
A) $0.0175$
B) $0.5542$
C) $0.6324$
D) $0.1389$

Question

Quizplus · Accepted Answer

The expression $\sin(\cos^{-1}(0.8324))$ can be solved by recognizing that $\cos^{-1}(0.8324)$ gives an angle whose cosine is 0.8324. Using the Pythagorean identity $\sin^2(x) + \cos^2(x) = 1$, we can find the sine of this angle. If $\cos(x) = 0.8324$, then $\sin(x) = \sqrt{1 - \cos^2(x)} = \sqrt{1 - 0.8324^2}$. Calculating this gives a value close to 0.5542, rounding to four decimal places.

Use a Calculator to Find the Value sin⁡(cos⁡−10.8324)\sin \left( \cos ^ { - 1 } 0.8324 \right)sin(cos−10.8324)

Use a Calculator to Find the Value $\sin \left( \cos ^ { - 1 } 0.8324 \right)$