1. Measuring Angles

Given an angle in standard position whose terminal side passes through the point $(1,1)$, what is the measure of angle $\mathrm{BAC}$? Round your answer to the nearest whole degree.

What is the angular position in radians of the minute hand of a clock at $5:00$, measured from the $12$ o'clock position in standard position (counterclockwise from the positive $x$-axis)?

If an angle in standard position has its terminal side passing through the point $(0,1)$ on the unit circle, what is its measure in degrees?

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.

I. N 70° W

II. 1. A. B. C. 2. 3. 4. D. E. F. 5. N 70° W 6. 7. G. H. 8. 9. 10. I. J.

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. - 70° 48'

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One degree, written 1°, represents ____________ of a complete rotation.

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I:

cos⁻¹ 0.45

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858

F. 1.962610506

G. 14.47751219°

H. 1.015426612

I. 1.051462224

J. 0.9925461516

Which of the following angle measures in degrees are coterminal with $45°$ in standard position?

If an angle in standard position has its terminal side passing through the point $(0,1)$ on the unit circle, what is the measure of the angle in degrees?

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.

I. 10. N 70° E

II. 1. A. B. C. 2. 3. 4. D. E. F. 5. 6. 7. G. H. 8. 9. I. J.

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

cot(90°-4.72°)

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-210°

Solve each problem. See Example 6. Revolutions of a Turntable A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second?

Find the measure of the smaller angle formed by the hands of a clock at the following times.