Answer
$\sin$(-855) = -$\frac{\sqrt2}{2}$
$\cos$(-855) = -$\frac{\sqrt2}{2}$
$\tan$(-855) = 1
$\cot$(-855) = 1
$\csc$(-855) = $-\sqrt2$
$\sec$(-855) = $-\sqrt2$
Work Step by Step
-855$^{\circ}$
We must first fine the coterminal angle:
-855$^{\circ}$ + 360$^{\circ}$ = -495$^{\circ}$
-495$^{\circ}$ + 360$^{\circ}$ = -135$^{\circ}$
-135$^{\circ}$ + 360$^{\circ}$ = 255$^{\circ}$
150 is in Quadrant III. Therefore all the trigonometric functions are negative with the exception of $\tan$ and $\cot$.
The reference angle is:
$\theta$$^{1}$ = 225$^{\circ}$ - 180$^{\circ}$ = 40$^{\circ}$
$\sin$(30) = -$\frac{1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$
$\cos$(30) = -$\frac{1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$
$\tan$(30) = $\frac{-1}{-1}$ = 1
$\cot$(30) = $\frac{-1}{-1}$ = 1
$\csc$(30) = -$\frac{\sqrt2}{1}$ = $-\sqrt2$
$\sec$(30) = -$\frac{\sqrt2}{1}$ = $-\sqrt2$
