QuestionFind the six trigonometric functions for the angle $-870^{\circ}$. Simplify your answer, including any radicals.

Studdy Solution
The cosecant, secant, and cotangent are the reciprocals of the sine, cosine, and tangent, respectively. So we have$$\csc(210^{\circ}) = -\csc(30^{\circ}) = -2$$$$\sec(210^{\circ}) = -\sec(30^{\circ}) = -\frac{2}{\sqrt{3}}$$$$\cot(210^{\circ}) = -\cot(30^{\circ}) = -\sqrt{3}$$Therefore, the exact values of the six trigonometric functions for $-870^{\circ}$ are the same as those for $210^{\circ}$.