Find principal value of Sin inverse 7 pi by 4

Explanation

To find the principal value of \(\sin^{-1}\left(\frac{7\pi}{4}\right)\), we will follow these steps:

### Step 1: Understand the Range of the Inverse Sine Function
The principal value of the inverse sine function, \(\sin^{-1}(x)\), is defined for \(x\) in the range \([-1, 1]\). Since \(\frac{7\pi}{4}\) is not in this range, we need to express it in a way that allows us to find its sine value.

**Hint:** Check if the angle is within the range of the sine function.

### Step 2: Rewrite the Angle
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