Answer
$2\sqrt2$
Work Step by Step
The terminal side of the angle $\dfrac{-\pi}{4}$ is in Quadrant IV.
This means its cosine value is positive.
The reference angle of an angle is equal to the smallest acute angle that its terminal side makes with the x-axis. The terminal side of $-\frac{\pi}{4}$ makes an $\frac{\pi}{4}$ angle with the positive x-axis.
Thus, the reference angle of the given angle is $\dfrac{\pi}{4}$.
Recall that an angle and its reference angle have the same cosine values, except possibly for their signs.
$\dfrac{\pi}{4}$ is a special angle whose cosine value if $\dfrac{\sqrt2}{2}$. Since $-\dfrac{\pi}{4}$ in Quadrant IV, its cosine is positive.
Therefore $\cos{(-\dfrac{\pi}{4})} = \dfrac{\sqrt2}{2}$.
Substitute this value into the given expression to obtain:
$4 \cos{\left(-\dfrac{\pi}{4}\right)}=4 \cdot \dfrac{\sqrt2}{2} = 2\sqrt2$
