The value of `cos^(-1)(cos ((3pi)/(2)))` is

Options

A. `pi/2`
B. `(3pi)/(2)`
C. `(5pi)/(2)`
D. `(7pi)/(2)`

Explanation

To find the value of \( \cos^{-1}(\cos(3\pi/2)) \), we can follow these steps:

### Step 1: Evaluate \( \cos(3\pi/2) \)
The angle \( 3\pi/2 \) radians corresponds to \( 270^\circ \). The cosine of \( 270^\circ \) is:
\[ \cos(3\pi/2) = 0 \]

### Step 2: Substitute into the inverse cosine function
Now, we substitute the value of \( \cos(3\pi/2) \) into the inverse cosine function:
\[ \cos^{-1}(\cos(3\pi/2)) = \cos^{-1}(0) \]

### Step 3: Find \( \cos^{-1}(0) \)
The value of \( \cos^{-1}(0) \) corresponds to the angle whose cosine is 0. The principal value of \( \cos^{-1}(0) \) is:
\[ \cos^{-1}(0) = \frac{\pi}{2} \]

### Final Answer
Thus, the value of \( \cos^{-1}(\cos(3\pi/2)) \) is:
\[ \frac{\pi}{2} \]

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