91Ó°ÊÓ

Exploration (a) Complete the table. \begin{tabular}{|l|l|l|l|l|l|} \hline\(\theta\) & \(0.1\) & \(0.2\) & \(0.3\) & \(0.4\) & \(0.5\) \\ \hline \(\sin \theta\) & & & & & \\ \hline \end{tabular} (b) Is \(\theta\) or \(\sin \theta\) greater for \(\theta\) in the interval \((0,0.5]\) ? (c) As \(\theta\) approaches 0 , how do \(\theta\) and \(\sin \theta\) compare? Explain.

The graph of \(y=\csc x\) can be obtained on a calculator by graphing the reciprocal of \(y=\sin x\).

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ -240^{\circ} $$

In Exercises 81-86, find two solutions of the equation. Give your answers in degrees \(\left(0^{\circ} \leq \theta<360^{\circ}\right)\) and in radians \((0 \leq \theta<2 \pi)\). Do not use a calculator. $$ \text { (a) } \sin \theta=\frac{1}{2} $$

In Exercises 81-86, find two solutions of the equation. Give your answers in degrees \(\left(0^{\circ} \leq \theta<360^{\circ}\right)\) and in radians \((0 \leq \theta<2 \pi)\). Do not use a calculator. (a) \(\cos \theta=\frac{\sqrt{2}}{2}\) (b) \(\cos \theta=-\frac{\sqrt{2}}{2}\)

The graph of \(y=\sec x\) can be obtained on a calculator by graphing a translation of the reciprocal of \(y=\sin x\).

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ 315^{\circ} $$

$$ \text { In Exercises 77-82, sketch a graph of the function. } $$ $$ f(x)=\arccos \frac{x}{4} $$

Exploration (a) Complete the table. \begin{tabular}{|l|l|l|l|l|l|l|} \hline\(\theta\) & \(0^{\circ}\) & \(18^{\circ}\) & \(36^{\circ}\) & \(54^{\circ}\) & \(72^{\circ}\) & \(90^{\circ}\) \\ \hline \(\sin \theta\) & & & & & & \\ \hline \(\cos \theta\) & & & & & & \\ \hline \end{tabular} (b) Discuss the behavior of the sine function for \(\theta\) in the range from \(0^{\circ}\) to \(90^{\circ}\). (c) Discuss the behavior of the cosine function for \(\theta\) in the range from \(0^{\circ}\) to \(90^{\circ}\). (d) Use the definitions of the sine and cosine functions to explain the results of parts (b) and (c).

In Exercises 83-88, use a graphing utility to graph the function. $$ f(x)=2 \arccos (2 x) $$