Answer
Next we find the reference angle:
180$^{\circ}$ - 135$^{\circ}$ = 45$^{\circ}$
$sin$(495)$^{\circ}$ = $\frac{\sqrt2}{2}$
$cos$(495)$^{\circ}$ = $\frac{-1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$
$tan$(495)$^{\circ}$ = $\frac{-1}{1}$ = -1
$cot$(495)$^{\circ}$ = $\frac{1}{-1}$ = -1
$csc$(495)$^{\circ}$ = $\frac{\sqrt2}{-1}$ = -$\sqrt2$
$sec$(495)$^{\circ}$ = $\frac{\sqrt2}{1}$ = $\sqrt2$
Work Step by Step
495$^{\circ}$
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.
495$^{\circ}$ - 360$^{\circ}$ = 135$^{\circ}$
Next we find the reference angle:
180$^{\circ}$ - 135$^{\circ}$ = 45$^{\circ}$
$sin$(45)$^{\circ}$ = $\frac{\sqrt2}{2}$
$cos$(45)$^{\circ}$ = $\frac{-1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$
$tan$(45)$^{\circ}$ = $\frac{-1}{1}$ = -1
$cot$(45)$^{\circ}$ = $\frac{1}{-1}$ = -1
$csc$(45)$^{\circ}$ = $\frac{\sqrt2}{-1}$ = -$\sqrt2$
$sec$(45)$^{\circ}$ = $\frac{\sqrt2}{1}$ = $\sqrt2$
