Chapter 14

Solve \(2 \sin ^{2} \theta=-\sin \theta\) for \(0 \leq \theta<2 \pi .\) Show your work.

Find the measure of an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$ 493^{\circ} $$

Simplify each expression. $$ \cos ^{2} \theta \sec \theta \csc \theta $$

Find the measure of an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$ -609^{\circ} $$

Simplify each expression. $$ \sin \theta \sec \theta \tan \theta $$

Make a box-and-whisker plot for each set of values. 300\(\quad 345 \quad 333 \quad 295 \quad 302 \quad 321\)

Simplify each expression. $$ \csc ^{2} \theta\left(1-\cos ^{2} \theta\right) $$

Make a box-and-whisker plot for each set of values. 3248\(\quad 87 \quad 43 \quad 62 \quad 15 \quad 49 \quad 51 \quad 47 \quad 36 \quad 50 \quad 109 \quad 64\)

Simplify each expression. $$ \frac{\cos \theta \csc \theta}{\cot \theta} $$

Simplify each expression. $$ \frac{\sec \theta}{\cot \theta+\tan \theta} $$

Simplify each expression. $$ \frac{\sin \theta+\tan \theta}{1+\cos \theta} $$

Write a cosine function for each description. amplitude \(4,\) period 8

Write a cosine function for each description. amplitude \(3,\) period 2\(\pi\)

Write a cosine function for each description. amplitude \(3 \pi,\) period 1

Write a cosine function for each description. amplitude \(\frac{\pi}{4},\) period 3\(\pi\)

Transportation Ninety-eight percent of a railroad's trains depart on schedule. Eighty-nine percent of its trains depart and arrive on schedule. Find the probability that a train that departs on time also arrives on time.