#### Answer

$\cos(-52^\circ14')$ is the cofunction in need to find here.

#### Work Step by Step

$$\sin(142^\circ14')$$
First, we must claim that cosine is the cofunction of sine.
Then we find the complementary angle $\theta$ for cosine to rewrite $\sin(142^\circ14')$, which must satisfy
$$\cos\theta=\sin(142^\circ14')\hspace{1cm}(1)$$
According to Cofunction Identity: $\cos\theta=\sin(90^\circ-\theta)$
Apply this to the equation $(1)$:
$$\sin(90^\circ-\theta)=\sin(142^\circ14')$$
$$90^\circ-\theta=142^\circ14'$$
$$\theta=90^\circ-142^\circ14'=-52^\circ14'$$
$\cos(-52^\circ14')$ is thus the cofunction in need to find here.