Answer
$\sin$(45) = $\frac{-\sqrt2}{2}$
$\cos$(45) = $\frac{\sqrt2}{2}$
$\tan$(45) = -1
$\cot$(45) = -1
$\csc$(45) = -$\sqrt2$
$\sec$(45) = $\sqrt2$
Work Step by Step
-2205$^{\circ}$
We must first fine the coterminal angle:
-2205$^{\circ}$ + 7(360$^{\circ}$) = 315$^{\circ}$
315 is in Quadrant IV. Therefore all the trigonometric functions are negative with the exception of $\cos$ and $\sec$.
The reference angle is:
$\theta$$^{1}$ = 360$^{\circ}$ - 315$^{\circ}$ = 45$^{\circ}$
$\sin$(45) = $\frac{-1}{\sqrt2}$ = $\frac{-\sqrt2}{2}$
$\cos$(45) = $\frac{1}{\sqrt2}$ = $\frac{\sqrt2}{2}$
$\tan$(45) = $\frac{-1}{1}$ = -1
$\cot$(45) = $\frac{1}{-1}$ = -1
$\csc$(45) = $\frac{\sqrt2}{-1}$ = -$\sqrt2$
$\sec$(45) = $\frac{\sqrt2}{1}$ = $\sqrt2$
