1. Measuring Angles

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

E

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

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 3 minutes and 40 seconds

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

In Exercises 8–12, draw each angle in standard position. 8𝜋 3

In Exercises 8–12, draw each angle in standard position. -135°

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

In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.

tan θ > 0 and sec θ > 0

In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.

tan θ > 0 and cos θ < 0

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

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

sin 38°

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

tan 32.7°

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

csc 17°