## Trigonometry (11th Edition) Clone

$\sec75^\circ36'$ is the co-function in need to find in this exercise.
$$\csc(14^\circ24')$$ First, we must claim that secant is the co-function of cosecant. Then we find the complementary angle $\theta$ for secant to rewrite $\csc(14^\circ24')$, which must satisfy $$\sec\theta=\csc(14^\circ24')\hspace{1cm}(1)$$ According to Co-function Identity: $\sec\theta=\csc(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\csc(90^\circ-\theta)=\csc(14^\circ24')$$ $$90^\circ-\theta=14^\circ24'$$ $$\theta=90^\circ-14^\circ24'=75^\circ36'$$ $\sec75^\circ36'$ is thus the co-function in need to find here.