Answer
-$sin$(1305)$^{\circ}$ = $\frac{-\sqrt2}{2}$
-$cos$(1305)$^{\circ}$ = $\frac{-\sqrt2}{2}$
$tan$(1305)$^{\circ}$ = 1
$cot$(1305)$^{\circ}$ = 1
-$csc$(1305)$^{\circ}$ = -$\sqrt2$
-$sec$(1305)$^{\circ}$ = -$\sqrt2$
Work Step by Step
1305$^{\circ}$
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.
1305$^{\circ}$ - 360$^{\circ}$ = 945$^{\circ}$
945$^{\circ}$ - 360$^{\circ}$ = 585$^{\circ}$
585$^{\circ}$ - 360$^{\circ}$ = 225$^{\circ}$
Next we must find the reference angle:
225$^{\circ}$ - 180$^{\circ}$ = 45$^{\circ}$
-$sin$(45)$^{\circ}$ = $\frac{-\sqrt2}{2}$
-$cos$(45)$^{\circ}$ = $\frac{-\sqrt2}{2}$
$tan$(45)$^{\circ}$ = $\frac{-\sqrt2}{-\sqrt2}$ = 1
$cot$(45)$^{\circ}$ = $\frac{-\sqrt2}{-\sqrt2}$ = 1
-$csc$(45)$^{\circ}$ = $\frac{-\sqrt2}{1}$ = -$\sqrt2$
-$sec$(45)$^{\circ}$ = $\frac{-\sqrt2}{1}$ = -$\sqrt2$
