1. Measuring Angles

Given that angle $xyz$ is in standard position and its terminal side passes through the point $(3,4)$, which is the best approximation for the measure of angle $xyz$ in degrees?

Given that angle $DFE$ is in standard position and its terminal side passes through the point $\left(4,,,3\right)$, what is the measure of angle $DFE$ to the nearest degree?

In the context of angles in standard position on the coordinate plane, which of the following pairs of angles are called coterminal angles?

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.

tan 421° 30'

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―90 °

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.

sin 38°

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.

120°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (-4, 0)

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One minute, written 1' , is ________________ of a degree.

Perform each calculation. See Example 3. 90° ― 36° 18' 47"

Find the measure of the smaller angle formed by the hands of a clock at the following times. 8:20

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.

3𝜋/4

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

csc θ = 1.3861147