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Find an angle between 0° and 360° that is coterminal with the given angle:
a. 2223°
b. -400°
c. 1270°
d. -800°
Solution:
Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side (angles less than 360°). Usually, coterminal angles are more than 360°. To simplify a coterminal angle, divide a given angle by 360° which is equivalent to 1 revolution. The remainder or a fraction of a revolution will be the terminal side. Let's have the examples of the following:
a. 2223°
Since the given angle is positive, then it is rotated counterclockwise from positive x-axis (initial side) to terminal side.
After six complete revolution from positive x-axis in a counterclockwise direction, there's an excess angle of
which is located at the first quadrant.
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| Photo by Math Principles in Everyday Life |
b. - 400°
Since the given angle is negative, then it is rotated clockwise from positive x-axis (initial side) to terminal side.
After one complete revolution from positive x-axis in a clockwise direction, there's an excess angle of
which is located at the fourth quadrant.
 |
| Photo by Math Principles in Everyday Life |
c. 1270°
Since the given angle is positive, then it is rotated counterclockwise from positive x-axis (initial side) to terminal side.
After three complete revolution from positive x-axis in a counterclockwise direction, there's an excess angle of
which is located at the third quadrant.
 |
| Photo by Math Principles in Everyday Life |
d. - 800°
Since the given angle is negative, then it is rotated clockwise from positive x-axis (initial side) to terminal side.
After two complete revolution from positive x-axis in a clockwise direction, there's an excess angle of
which is located at the fourth quadrant.
 |
| Photo by Math Principles in Everyday Life |