Question

Evaluate:sin^-1(cos(7pi/4))

Answer 1

SOLUTION

Given the expression in the question tab, the following are the solution steps to get the answer

Step 1: Write out the expression

$\sin ^{-1}(\cos (\frac{7\pi}{4}))$

Step 2: Evaluate the expression using the order of operation. This implies that we evaluate the bracket first.

$\begin{gathered} \sin ^{-1}(\cos (\frac{7\pi}{4})) \\ \text{solving }(\cos (\frac{7\pi}{4})),\text{ we have} \\ \cos (5.497787144) \\ =0.9953998993 \end{gathered}$

Step 3: We evaluate the last part of the expression

$\begin{gathered} \sin ^{-1}(\cos (\frac{7\pi}{4}))=\sin ^{-1}(0.9953998993) \\ =84.50221286 \\ \sin ^{-1}(\cos (\frac{7\pi}{4}))\approx84.5022 \end{gathered}$

Hence, the result from the evaluation of sin^-1(cos(7pi/4)) is approximately 84.5022.