Answer
(a) $\sin$ 38$^{\circ}$
(b) $\cot$ 19$^{\circ}$
(c) $\csc$ 66$^{\circ}$
Work Step by Step
The cofunction uses Trigonometric Identities to show the relationship between Trigonometric Functions. Below shows the following relationship between common functions:
$\sin$(90$^{\circ}$ - x) = $\cos$ x
$\cos$(90$^{\circ}$ - x) = $\sin$ x
$\tan$(90$^{\circ}$ - x) = $\cot$ x
$\cot$(90$^{\circ}$ - x) = $\tan$ x
$\sec$(90$^{\circ}$ - x) = $\csc$ x
$\csc$(90$^{\circ}$ - x) = $\sec$ x
Therefore:
(a) $\cos$ 52$^{\circ}$ = $\sin$(90$^{\circ}$ - 52$^{\circ}$) = $\sin$ 38$^{\circ}$
(b) $\tan$ 71$^{\circ}$ = $\cot$(90$^{\circ}$ - 71$^{\circ}$) = $\cot$ 19$^{\circ}$
(b) $\sec$ 24$^{\circ}$ = $\csc$(90$^{\circ}$ - 24$^{\circ}$) = $\csc$ 66$^{\circ}$
