Answer
$sin$(480)$^{\circ}$ = $\frac{\sqrt3}{2}$
$cos$(480)$^{\circ}$ = $\frac{-1}{2}$
$tan$(480)$^{\circ}$ = -$\sqrt3$
$cot$(480)$^{\circ}$ = -$\frac{\sqrt3}{3}$
$csc$(480)$^{\circ}$ = $\frac{2\sqrt3}{\sqrt3}$
$sec$(480)$^{\circ}$ = -2
Work Step by Step
480$^{\circ}$
We can solve for the functions by using the coterminal angle. We can find the coterminal angle by adding or subtracting 360$^{\circ}$ as many times as needed.
480$^{\circ}$ - 360$^{\circ}$ = 120$^{\circ}$
Next we find the reference angle:
180$^{\circ}$ - 120$^{\circ}$ = 60$^{\circ}$
$sin$(60)$^{\circ}$ = $\frac{\sqrt3}{2}$
$cos$(60)$^{\circ}$ = $\frac{-1}{2}$
$tan$(60)$^{\circ}$ = $\frac{\sqrt3}{-1}$ = -$\sqrt3$
$cot$(60)$^{\circ}$ = $\frac{-1}{\sqrt3}$ = -$\frac{\sqrt3}{3}$
$csc$(60)$^{\circ}$ = $\frac{2}{\sqrt3}$ = $\frac{2\sqrt3}{\sqrt3}$
$sec$(60)$^{\circ}$ = $\frac{2}{-1}$ = -2
