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# The value of $\cos^{-1}\bigg(\cos\frac{3\pi}{2}\bigg)$ is equal to:

$(A)\quad\frac{\pi}{2}\quad(B)\quad\frac{3\pi}{2}\quad(C)\quad\frac{5\pi}{2}\quad(D)\quad\frac{7\pi}{2}$

Toolbox:
• Principal interval of cos is $[0,\pi]$
• sin0=0
• $cos^{-1}0=\large\frac{\pi}{2}$
• $cos\large\frac{3\pi}{2}=0$
Ans (A) $\large\frac{\pi}{2}$
$\large\frac{3\pi}{2}$ is not in the principal interval.
$cos\large\frac{3\pi}{2}=0$
$\Rightarrow\:cos^{-1}\: cos\large\frac{3\pi}{2}=cos^{-1}0=\large\frac{\pi}{2}$

edited Mar 16, 2013