Answer
$-1$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant- II: $180^{\circ}-\theta $
c) Quadrant -III: $\theta - 180^o $
d) Quadrant -IV: $360^{\circ}-\theta $
Now, Step : (a) refers to: $=\dfrac{\pi}{4}$
Reference angle is equal to
$ =\dfrac{\pi}{4}$
Since, $\tan (\dfrac{\pi}{4})=1$
So, $\tan \dfrac{-\pi}{4}=-1$; Because $\theta $ lies in Quadrant-IV.
