91Ó°ÊÓ

Determine the angle of the smallest possible positive measure that is coterminal with each of the following angles. $$ 1395^{\circ} $$

Simplify each of the following expressions if possible. Leave all answers in terms of \(\sin \theta\) and \(\cos \theta .\) \(\sec \theta-\cos \theta\)

What is the measure of the angle swept out by the hour hand if it starts at 3 P.M. on Wednesday and continues until 5 P.M. on Thursday.

Find all possible values of \(\theta\), where \(0^{\circ}<\theta \leq 360^{\circ}\), when each of the following is true. $$ \sin \theta=-1 $$

In Exercises 65 and 66, explain the mistake that is made. Find the angle with smallest positive measure that is coterminal with the angle with measure \(-45^{\circ}\). Assume that both angles are in standard position. Solution: Coterminal angles are supplementary angles. \(-45^{\circ}+\alpha=180^{\circ}\) Add \(45^{\circ}\) to both sides. \(\alpha=225^{\circ}\) This is incorrect. What mistake was made?

In Exercises 67-76, use a calculator to evaluate the following expressions. If you get an error, explain why.\(\cos 270^{\circ}\)

Write \(\cot \theta\) in terms of only \(\sin \theta\).

Use a calculator to evaluate the following expressions. If you get an error, explain why. \(\sec 270^{\circ}\)

Find the smallest possible positive measure of \(\theta\) (rounded to the nearest degree) if the indicated information is true. \(\sin \theta=-0.1746\) and the terminal side of \(\theta\) lies in quadrant III.

Write in terms of \(\sin \theta: \frac{\cos \theta}{\tan \theta(1-\sin \theta)}\).