which is equivalent to \\( \\cos^{-1}(0) \\)? give your answer in radians. 0 \\( \\frac{\\pi}{2} \\) \\(…
which is equivalent to \\( \\cos^{-1}(0) \\)? give your answer in radians. 0 \\( \\frac{\\pi}{2} \\) \\( \\pi \\) \\( 2\\pi \\)
Answer
Answer:
$\frac{\pi}{2}$
Explanation:
Step1: Recall the definition of inverse cosine function
The inverse cosine function, $y = \cos^{-1}(x)$, gives the angle $y$ in the interval $[0,\pi]$ such that $\cos(y)=x$.
Step2: Find the angle $y$ for $x = 0$
We know that $\cos\left(\frac{\pi}{2}\right)=0$ and $\frac{\pi}{2}\in[0,\pi]$. So, $\cos^{-1}(0)=\frac{\pi}{2}$.