91Ó°ÊÓ

Complete the table with exact trigonometric function values. Do not use a calculator. $$\begin{array}{|c|c|c|c|c|c|c|} \hline \theta & \sin \theta & \cos \theta & \tan \theta & \cot \theta & \sec \theta & \csc \theta \\ \hline 60^{\circ} & & \frac{1}{2} & \sqrt{3} & & 2 & \\ \hline \end{array}$$

Find (a) the complement and (b) the supplement of each angle. Do not use a calculator. $$\frac{\pi}{4}$$

Rationalize the denominators for the given expressions. Assume all expressions containing \(x\) are positive. $$\frac{1}{2 \sqrt{5}}$$

Use the even-odd identities to write of the following expressions as a trigonometric function of a positive number $$\tan \left(-\frac{\pi}{7}\right)$$

To show that sec(- \(x\) ) = sec \(x\) for all \(x\) in the domain, we begin by writing $$ \sec (-x)=\frac{1}{\cos (-x)} $$ and then use the fact that \(\cos (-x)=\cos x\) for all \(x\) to complete the argument. Use this method to prove each of the following. $$\sec (-x)=\sec x$$

Determine what fraction of the circumference of the unit circle each value of s represents. For example, \(s=\pi\) represents \(\frac{1}{2}\) of the circumference of the unit circle. Do not use a calculator. $$s=\frac{5 \pi}{4}$$

Complete the table with exact trigonometric function values. Do not use a calculator. $$\begin{array}{|c|c|c|c|c|c|c|} \hline \theta & \sin \theta & \cos \theta & \tan \theta & \cot \theta & \sec \theta & \csc \theta \\ \hline 120^{\circ} & \frac{\sqrt{3}}{2} & & -\sqrt{3} & & & \frac{2 \sqrt{3}}{3} \\ \hline \end{array}$$

To show that sec(- \(x\) ) = sec \(x\) for all \(x\) in the domain, we begin by writing $$ \sec (-x)=\frac{1}{\cos (-x)} $$ and then use the fact that \(\cos (-x)=\cos x\) for all \(x\) to complete the argument. Use this method to prove each of the following. $$\csc (-x)=-\csc x$$

Rationalize the denominators for the given expressions. Assume all expressions containing \(x\) are positive. $$\frac{1}{3 \sqrt{7}}$$

Determine what fraction of the circumference of the unit circle each value of s represents. For example, \(s=\pi\) represents \(\frac{1}{2}\) of the circumference of the unit circle. Do not use a calculator. $$s=\frac{7 \pi}{6}$$