Problem

If an angle \(\theta\) in standard position has a measure of \(\frac{7\pi}{6}\) radians, find its supplement.

Answer

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Answer

However, an angle cannot be negative. Thus, we add \(2\pi\) to the result, which gives us \(-\frac{\pi}{6} + 2\pi = \frac{11\pi}{6}\).

Steps

Step 1 ：First, we know that the supplement of an angle \(\theta\) is \(\pi - \theta\).

Step 2 ：Substitute \(\frac{7\pi}{6}\) into the formula to get the supplementary angle, which gives us \(\pi - \frac{7\pi}{6} = \frac{6\pi}{6} - \frac{7\pi}{6} = -\frac{\pi}{6}\).

Step 3 ：However, an angle cannot be negative. Thus, we add \(2\pi\) to the result, which gives us \(-\frac{\pi}{6} + 2\pi = \frac{11\pi}{6}\).

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