Understanding Coterminal Angles and How to Determine Them

TLDR; Coterminal angles have the same terminal side. Angles can be determined to be coterminal by adding or subtracting multiples of 360 degrees.

Coterminal angles are two angles in standard position that have the same terminal side.

The speaker explains that to determine if two angles are coterminal, they should have the same terminal side in standard position.

This concept sets the stage for understanding how to determine if two angles are coterminal.

The speaker sketches 132 degrees and -588 degrees in standard position to visually represent their terminal sides.

For 132 degrees, the initial side is along the positive X-axis, then rotated counterclockwise 132 degrees.

For -588 degrees, the terminal side is along the positive X-axis, then rotated clockwise 588 degrees.

By rotating -588 degrees, it's determined that it ends up on the same terminal side as 132 degrees.

This is shown by adding and subtracting multiples of 360 degrees to obtain the other coterminal angles.

The speaker explains that if two angles are coterminal, adding and subtracting multiples of 360 degrees will lead to the other coterminal angles.

For example, adding 360 degrees to -588 degrees gives -228 degrees, which is coterminal to -588 degrees.

Similarly, adding 360 degrees again to -228 degrees gives 132 degrees, proving that the angles are coterminal.

To determine a coterminal angle with any angle theta, the coterminal angle would measure theta + 360 degrees x K, where K is an integer.

If K is negative, it's equivalent to subtracting multiples of 360, and if K is positive, it's equivalent to adding multiples of 360 degrees.