Question

Two angles with the same initial and terminal sides but possibly different rotations are called​ __________ angles. Increasing or decreasing the degree measure of an angle in standard position by an integer multiple of ​ ______ results in such an angle. Increasing or decreasing the radian measure of an angle in standard position by an integer multiple of​ ________ results in such an angle.

Answer 1

Two angles with the same initial and terminal sides but possibly different rotations are called​ Coterminal angles. Increasing or decreasing the degree measure of an angle in standard position by an integer multiple of ​ 360° results in such an angle. Increasing or decreasing the radian measure of an angle in standard position by an integer multiple of​ 2π results in such an angle.

Explanation:

Two angles in the same position are called corresponding angles. They have the same measure if the original two lines are parallel.

Answer 2

Two angles with the same initial and terminal sides but possibly different rotations are called​ Coterminal angles. Increasing or decreasing the degree measure of an angle in standard position by an integer multiple of ​ 360° results in such an angle. Increasing or decreasing the radian measure of an angle in standard position by an integer multiple of​ 2π results in such an angle.

Explanation:

Consider the provided information.

Coterminal angles are angles that share the same sides of the initial and terminal. Depending on whether the given angle is in degrees or radians, calculating coterminal angles is as simple as adding or subtracting 360° or 2π to each angle. An angle of θ° is coterminal with angles of θ±360°k, where k is an integer.

Now fill the blanks as shown:

Two angles with the same initial and terminal sides but possibly different rotations are called​ Coterminal angles. Increasing or decreasing the degree measure of an angle in standard position by an integer multiple of ​ 360° results in such an angle. Increasing or decreasing the radian measure of an angle in standard position by an integer multiple of​ 2π results in such an angle.