Answer
$\dfrac{\pi}{4}$
Work Step by Step
RECALL:
The following are the means on how to find the reference angle of an angle $\theta$ based on its position:
(1) Quadrant I: $\theta$ (itself)
(2) Quadrant II: $\pi-\theta$
(3) Quadrant III: $\theta - \pi$
(4) Quadrant IV: $2\pi-\theta$
$\frac{7\pi}{4}$ is in Quadrant IV.
Thus, using formula (4) above gives:
reference angle of $\frac{7\pi}{4}$ = $2\pi-\dfrac{7\pi}{4}=\dfrac{8\pi}{4}-\dfrac{7\pi}{4} = \dfrac{\pi}{4}$
