1. Measuring Angles

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

tan 32.7°

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.

-5𝜋/4

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. 274° 18' 59"

In Exercises 8–12, draw each angle in standard position. 5𝜋 6

Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3

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.

cos θ = 0.85536428

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 8440°

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. -25.485°

What is the approximate measure of the angle shown below? Choose the most reasonable answer.

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. cos θ = 0.4112

Given a point $(3,4)$ on the terminal side of an angle $\angle$ in standard position, what is the measure of angle $ACB$ in degrees?

Given two intersecting lines in the coordinate plane, which diagram shows angles $1$ and $2$ as vertical angles in standard position?

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. cot θ = 0.21563481