91Ó°ÊÓ

In Exercises 59-68, write an algebraic expression that is equivalent to the expression. (Hint: Sketch a right triangle, as demonstrated in Example 7.) $$ \sec (\arctan 3 x) $$

Convert the angle measure from degrees to radians. Round to three decimal places. $$0.54^{\circ}$$

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

In Exercises 59-64, find the indicated trigonometric value in the specified quadrant. $$ \csc \theta=-2 $$ $$ \begin{array}{cc} \text { Quadrant } & \text { Trigonometric Value } \\ \text { IV } & \cos \theta \\ \text { II } & \sin \theta \\ \text { III } & \sec \theta \\ \text { IV } & \cot \theta \\ \text { I } & \sec \theta \\ \text { III } & \tan \theta \end{array} $$

Use the unit circle to verify that the cosine and secant functions are even and that the sine, cosecant, tangent, and cotangent functions are odd.

\(y=\frac{1}{100} \sin 120 \pi t\)

Convert the angle measure from radians to degrees. Round to three decimal places. $$\frac{\pi}{7}$$

\(f(x)=\sin ^{2} x, \quad g(x)=\frac{1}{2}(1-\cos 2 x)\)

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 \(\boldsymbol{\theta}\). $$ (x, 4 x), x>0 $$

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