Question

which equation can be used to determine the reference angle, r, if \\(\theta = \frac{7\pi}{12}\\)?
\\(\bigcirc\\) \\(r = \theta\\)
\\(\bigcirc\\) \\(r = \pi - \theta\\)
\\(\bigcirc\\) \\(r = \theta - \pi\\)
\\(\bigcirc\\) \\(r = 2\pi - \theta\\)

Explanation:

Step1: Identify quadrant of θ

$\frac{\pi}{2} < \frac{7\pi}{12} < \pi$ (since $\frac{\pi}{2}=\frac{6\pi}{12}$, $\pi=\frac{12\pi}{12}$), so θ is in Quadrant II.

Step2: Reference angle formula for Quadrant II

Reference angle $r = \pi - \theta$.

Answer:

B. $r = \pi - \theta$