Answer
$sin$(570)$^{\circ}$ = $\frac{-1}{2}$
$cos$(570)$^{\circ}$ = $\frac{-\sqrt3}{2}$
$tan$(570)$^{\circ}$ = $\frac{1}{\sqrt3}$ = $\frac{\sqrt3}{3}$
$cot$(570)$^{\circ}$ = $\frac{\sqrt3}{1}$ = $\sqrt3$
$csc$(570)$^{\circ}$ = $\frac{2}{-1}$ = -2
$sec$(570)$^{\circ}$ = $\frac{2}{-\sqrt3}$ = $\frac{2\sqrt3}{3}$
Work Step by Step
570$^{\circ}$
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.
570$^{\circ}$ - 360$^{\circ}$ = 210$^{\circ}$
Next we find the reference angle:
210$^{\circ}$ - 180$^{\circ}$ = 30$^{\circ}$
-$sin$(30)$^{\circ}$ = $\frac{-1}{2}$
-$cos$(30)$^{\circ}$ = $\frac{-\sqrt3}{2}$
$tan$(30)$^{\circ}$ = $\frac{1}{\sqrt3}$ = $\frac{\sqrt3}{3}$
$cot$(30)$^{\circ}$ = $\frac{\sqrt3}{1}$ = $\sqrt3$
-$csc$(30)$^{\circ}$ = $\frac{2}{-1}$ = -2
-$sec$(30)$^{\circ}$ = $\frac{2}{-\sqrt3}$ = $\frac{2\sqrt3}{3}$
