91Ó°ÊÓ

Construct an appropriate triangle to complete the table. \(\left(0^{\circ} \leq \theta \leq 90^{\circ}, 0 \leq \theta \leq \pi / 2\right)\) $$\begin{array}{llll} \text {Function} & \theta(\operatorname{deg}) & \theta(\mathrm{rad}) & \text {Function Value} \\ \cos & \square & \frac{\pi}{6} & \square \end{array}$$

Describe the relationship between the graphs of \(f\) and \(g .\) Consider amplitudes, periods, and shifts. $$\begin{array}{l} f(x)=\sin x \\ g(x)=5 \sin (-x) \end{array}$$

State the quadrant in which \(\theta\) lies. $$\sin \theta < 0 \text { and } \cos \theta < 0$$

Sketch the graph of the function. (Include two full periods.) Use a graphing utility to verify your result. \(y=2 \cot \left(x+\frac{\pi}{2}\right)\)

Determine two coterminal angles in degree measure (one positive and one negative) for each angle. (There are many correct answers). (a) \(300^{\circ}\) (b) \(-740^{\circ}\)

Use a calculator to approximate the value of the expression, if possible. Round your answer to the nearest hundredth. arctan (-6)

Use a calculator to approximate the value of the expression, if possible. Round your answer to the nearest hundredth. \(\tan ^{-1} 5.9\)

Describe the relationship between the graphs of \(f\) and \(g .\) Consider amplitudes, periods, and shifts. $$\begin{aligned} &f(x)=\sin x\\\ &g(x)=-\frac{1}{2} \sin x \end{aligned}$$

Determine two coterminal angles in degree measure (one positive and one negative) for each angle. (There are many correct answers). (a) \(-445^{\circ}\) (b) \(230^{\circ}\)

Construct an appropriate triangle to complete the table. \(\left(0^{\circ} \leq \theta \leq 90^{\circ}, 0 \leq \theta \leq \pi / 2\right)\) $$\begin{array}{llll} \text {Function} & \theta(\operatorname{deg}) & \theta(\mathrm{rad}) & \text {Function Value} \\ \sin & \square & \frac{\pi}{4} & \square \end{array}$$