Trigonometry (10th Edition)

$\sin$(-1290) = $\frac{1}{2}$ $\cos$(-1290) = -$\frac{\sqrt3}{2}$ $\tan$(-1290) = -$\frac{\sqrt3}{3}$ $\cot$(-1290) = 2 $\csc$(-1290) = -$\frac{2\sqrt3}{3}$ $\sec$(-1290) = -$\sqrt3$
-1290$^{\circ}$ We must first fine the coterminal angle: -1290$^{\circ}$ + 360$^{\circ}$ = -930$^{\circ}$ -930$^{\circ}$ + 360$^{\circ}$ = -570$^{\circ}$ -570$^{\circ}$ + 360$^{\circ}$ = -210$^{\circ}$ -210$^{\circ}$ + 360$^{\circ}$ = 150$^{\circ}$ 150 is in Quadrant II. Therefore all the trigonometric functions are negative with the exception of $\sin$ and $\csc$. The reference angle is: $\theta$$^{1}$ = 180$^{\circ}$ - 150$^{\circ}$ = 30$^{\circ}$ $\sin$(30) = $\frac{1}{2}$ $\cos$(30) = -$\frac{\sqrt3}{2}$ $\tan$(30) = -$\frac{\sqrt3}{3}$ $\cot$(30) = 2 $\csc$(30) = -$\frac{2\sqrt3}{3}$ $\sec$(30) = -$\sqrt3$