91Ó°ÊÓ

Find the values of the six trigonometric functions of \(\theta\).$$ \begin{array}{ll} \text { Function Value } & \text { Constraint } \\ \text { } \csc \theta=\frac{3}{2} & \cos \theta<0 \\ \end{array} $$

Find the values of the six trigonometric functions of \(\theta\).$$ \begin{array}{ll} \text { Function Value } & \text { Constraint } \\ \text { } \sin \theta=\frac{3}{8} & \cos \theta<0 \\\\\end{array} $$

In Exercises 59-68, write an algebraic expression that is equivalent to the expression. (Hint: Sketch a right triangle, as demonstrated in Example 7.) $$ \csc \left(\arctan \frac{x}{\sqrt{2}}\right) $$

\(f(x)=x^{3} \sin x\)

Convert the angle measure from radians to degrees. Round to three decimal places. $$-4.2 \pi$$

In Exercises 65-80, use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \cos \left(-110^{\circ}\right) $$

Find the values of the six trigonometric functions of \(\theta\).$$ \begin{array}{ll} \text { Function Value } & \text { Constraint } \\ \text { } \tan \theta=\frac{5}{4} & \cos \theta<0 \\ \end{array} $$

Convert the angle measure from radians to degrees. Round to three decimal places. $$4.8 \pi$$

\(h(x)=x^{3} \cos x\)

In Exercises 65-80, use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \csc \left(-330^{\circ}\right) $$