91Ó°ÊÓ

In Exercises 59-64, find the indicated trigonometric value in the specified quadrant. $$ \cot \theta=-3 $$ $$ \begin{array}{cc} \text { Quadrant } & \text { Trigonometric Value } \\ \text { IV } & \cos \theta \\ \text { II } & \sin \theta \\ \text { III } & \sec \theta \\ \text { IV } & \cot \theta \\ \text { I } & \sec \theta \\ \text { III } & \tan \theta \end{array} $$

\(y=3 \cos \left(\frac{\pi x}{2}+\frac{\pi}{2}\right)-2\)

The point is on the terminal side of an angle \(\theta\) in standard position. Determine the exact values of the six trigonometric functions of the angle \(\boldsymbol{\theta}\). $$ \left(-\frac{10}{3},-\frac{2}{3}\right) $$

\(y=-0.1 \sin \left(\frac{\pi x}{10}+\pi\right)\)

Exploration Let \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) be points on the unit circle corresponding to \(t=t_{1}\) and \(t=\pi-t_{1}\), respectively. (a) Identify the symmetry of the points \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). (b) Make a conjecture about any relationship between \(\sin t_{1}\) and \(\sin \left(\pi-t_{1}\right)\). (c) Make a conjecture about any relationship between \(\cos t_{1}\) and \(\cos \left(\pi-t_{1}\right)\).

\(f(x)=\sin x+\cos \left(x+\frac{\pi}{2}\right), \quad g(x)=0\)

The point is on the terminal side of an angle \(\theta\) in standard position. Determine the exact values of the six trigonometric functions of the angle \(\boldsymbol{\theta}\). $$ (-0.5,4.5) $$

In Exercises 59-68, write an algebraic expression that is equivalent to the expression. (Hint: Sketch a right triangle, as demonstrated in Example 7.) $$ \cos (\arcsin 2 x) $$

Convert the angle measure from degrees to radians. Round to three decimal places. $$-0.83^{\circ}$$

The point is on the terminal side of an angle \(\theta\) in standard position. Determine the exact values of the six trigonometric functions of the angle \(\boldsymbol{\theta}\). $$ (0.3,0.4) $$