Question

for the given angle $\theta$, identify the reference angle, $\varphi$
$\theta = \frac{11\pi}{6}$ $\varphi = ?$
$\circ \frac{\pi}{6}$
$\circ \frac{\pi}{3}$
$\circ 2\pi$

Explanation:

Step1: Determine quadrant of θ

$θ=\frac{11π}{6}$ is between $\frac{3π}{2}(=2.5π)$ and $2π$, so it is in Quadrant IV.

Step2: Calculate reference angle

For Quadrant IV, reference angle $\varphi=2π-θ$.
$\varphi=2π-\frac{11π}{6}=\frac{12π}{6}-\frac{11π}{6}=\frac{π}{6}$.

Answer:

$\frac{π}{6}$