91Ó°ÊÓ

Evaluate each of the following expressions when \(x\) is \(\pi / 6\). In each case, use exact values. $$ 4 \cos \left(2 x+\frac{\pi}{3}\right) $$

If we start at the point \((1,0)\) and travel once around the unit circle, we travel a distance of \(2 \pi\) units and arrive back where we started. If we continue around the unit circle a second time, we will repeat all the values of \(x\) and \(y\) that occurred during our first trip around. Use this discussion to evaluate the following expressions: $$ \sin \left(2 \pi+\frac{\pi}{2}\right) $$

Find \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), given the following information. \(\tan \theta=1\) and \(\theta\) in QIII

Evaluate each of the following expressions when \(x\) is \(\pi / 6\). In each case, use exact values. $$ -\frac{1}{2} \sin \left(3 x+\frac{\pi}{6}\right) $$

If we start at the point \((1,0)\) and travel once around the unit circle, we travel a distance of \(2 \pi\) units and arrive back where we started. If we continue around the unit circle a second time, we will repeat all the values of \(x\) and \(y\) that occurred during our first trip around. Use this discussion to evaluate the following expressions: $$ \cos \left(2 \pi+\frac{\pi}{4}\right) $$

If we start at the point \((1,0)\) and travel once around the unit circle, we travel a distance of \(2 \pi\) units and arrive back where we started. If we continue around the unit circle a second time, we will repeat all the values of \(x\) and \(y\) that occurred during our first trip around. Use this discussion to evaluate the following expressions: $$ \sin \left(2 \pi+\frac{\pi}{6}\right) $$

Find \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), given the following information. \(\sec \theta=-2\) with \(\theta\) in QII

Evaluate each of the following expressions when \(x\) is \(\pi / 6\). In each case, use exact values. $$ 4-\frac{2}{3} \sin (3 x-\pi) $$

Evaluate each of the following expressions when \(x\) is \(\pi / 6\). In each case, use exact values. $$ -1+\frac{3}{4} \cos \left(4 x-\frac{\pi}{2}\right) $$

Find \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), given the following information. \(\csc \theta=-2\) with \(\theta\) in QIII