1. Measuring Angles

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 122.6853°

Find the measure of each marked angle. See Example 2 supplementary angles with measures 6𝓍 - 4 and 8𝓍 - 12 degrees

Solve each problem. Rotating Pulley A pulley is rotating 320 times per min. Through how many degrees does a point on the edge of the pulley move in 2/3 sec?

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.

16𝜋/3

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 183° 48'

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 55 seconds

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

Column I: 1.

csc⁻¹ 4

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

Consider the equation $\sin \theta$. If $\theta$ is an angle in Quadrant IV, what is the value of $\sin \theta$?

Solve each problem. See Example 6. Rotating Pulley A pulley rotates through 75° in 1 min. How many rotations does the pulley make in 1 hr?

If angle $CBD$ has a measure of $140°$, what is the measure of angle $ABD$ if point $A$ lies on the terminal side of angle $CBD$ such that $A$, $B$, and $D$ are collinear and $B$ is the vertex?

Given that angle $xyz$ is in standard position and its terminal side passes through the point $(40,28)$, which is the best approximation for the measure of angle $xyz$ in degrees?

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 1000°

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

I. S 70° W

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

Given a circle with center $O$ and points $Q$, $S$, and $R$ on the circumference such that angle $QOR$ is $60°$, what is the measure of arc $QSR$ in degrees?