Answer
$sin$(420)$^{\circ}$ = $\frac{\sqrt3}{2}$
$cos$(420)$^{\circ}$ = $\frac{1}{2}$
$tan$(420)$^{\circ}$ =$\sqrt3$
$cot$(420)$^{\circ}$ = $\frac{\sqrt3}{3}$
$sec$(420)$^{\circ}$ = $\frac{2\sqrt3}{\sqrt3}$
$csc$(420)$^{\circ}$ = 2
Work Step by Step
420$^{\circ}$
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.
420$^{\circ}$ - 360$^{\circ}$ = 60$^{\circ}$
$sin$(60)$^{\circ}$ = $\frac{\sqrt3}{2}$
$cos$(60)$^{\circ}$ = $\frac{1}{2}$
$tan$(60)$^{\circ}$ = $frac{\sqrt3}{1}$ =$\sqrt3$
$cot$(60)$^{\circ}$ = $\frac{1}{\sqrt3}$ = $\frac{sqrt3}{3}$
$sec$(60)$^{\circ}$ = $\frac{2}{\sqrt3}$ = $\frac{2\sqrt3}{\sqrt3}$
$csc$(60)$^{\circ}$ = $\frac{2}{1}$ = 2
