91Ó°ÊÓ

Simplify each expression by substituting values from the table of exact values and then simplifying the resulting expression. $$\sin 30^{\circ} \cos 60^{\circ}$$

For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). $$ y=-3+\sin x \quad \text { for } x=0, \frac{\pi}{2}, \pi, \frac{3 \pi}{2}, 2 \pi $$

For Problems 83 through 94 , determine if the statement is possible for some real number \(z\). $$ \cot z=0 $$

For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). $$ y=3 \sin \left(2 x+\frac{\pi}{2}\right) \quad \text { for } x=-\frac{\pi}{4}, 0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4} $$

For Problems 83 through 94 , determine if the statement is possible for some real number \(z\). $$ \sec z=\frac{1}{2} $$

For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). $$ y=5 \cos \left(2 x-\frac{\pi}{3}\right) \quad \text { for } x=\frac{\pi}{6}, \frac{\pi}{3}, \frac{2 \pi}{3}, \pi, \frac{7 \pi}{6} $$

Simplify each expression by substituting values from the table of exact values and then simplifying the resulting expression. $$\left(\sin 45^{\circ}+\cos 45^{\circ}\right)^{2}$$

For Problems 83 through 94 , determine if the statement is possible for some real number \(z\). $$ \csc z=0 $$

These questions are available to help instructors assess if you have successfully met the learning objectives for this section. Give the reference angle for \(153^{\circ}\). a. \(27^{\circ}\) b. \(63^{\circ}\) c. \(-27^{\circ}\) d. \(-63^{\circ}\)

These questions are available to help instructors assess if you have successfully met the learning objectives for this section. Use a reference angle to find the exact value of \(\cos 210^{\circ}\). a. \(-\frac{1}{2}\) b. \(-\frac{\sqrt{3}}{2}\) c. \(-\frac{\sqrt{2}}{2}\) d. \(\frac{1}{2}\)