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A positive coterminal angle is any angle that is coterminal with a given angle where the measure is greater than 0 degrees. To find a positive coterminal angle, you add multiples of 360 degrees to the original angle.
For example, if you have an angle of 300 degrees, adding one multiple of 360 degrees gives you:

\[300^{\text{°}} + 360^{\text{°}} = 660^{\text{°}} \]
This means 660 degrees is a positive coterminal angle of 300 degrees.
If you add another multiple of 360 degrees:

\[660^{\text{°}} + 360^{\text{°}} = 1020^{\text{°}} \]
You get 1020 degrees, another positive coterminal angle. Positive coterminal angles are useful when you need to find equivalent angles that are greater than the original. They help in various applications like trigonometry and physics.

A negative coterminal angle is any angle that is coterminal with a given angle where the measure is less than 0 degrees. To find a negative coterminal angle, you subtract multiples of 360 degrees from the original angle.
Considering an angle of 300 degrees:

\[300^{\text{°}} - 360^{\text{°}} = -60^{\text{°}} \]
This provides a negative coterminal angle of -60 degrees.
For another negative coterminal angle, subtract 360 degrees again:

\[ -60^{\text{°}} - 360^{\text{°}} = -420^{\text{°}} \]
Thus, -420 degrees is another negative coterminal angle. Negative coterminal angles are essential when dealing with rotations or when needing angles within a full circle's range in negative direction.

Adding multiples of 360 degrees means you repeatedly add 360 degrees to an angle to find coterminal angles. Since 360 degrees equals one full rotation around a circle, adding it to any angle brings you back to the same terminal side.
To find positive coterminal angles, start with your original angle and add 360 degrees:

• If the angle is 300 degrees:

\[300^{\text{°}} + 360^{\text{°}} = 660^{\text{°}} \]
Add another 360 degrees:

• From 660 degrees:

\[660^{\text{°}} + 360^{\text{°}} = 1020^{\text{°}} \]
Adding multiples of 360 degrees is mainly used to keep angles within a manageable range while maintaining their geometric relationships.

Subtracting multiples of 360 degrees involves taking away 360 degrees from an angle repeatedly to find negative coterminal angles. This operation is crucial when you need angles in the negative measurement range.
For instance, if you start with an angle of 300 degrees:

• Subtract 360 degrees:

\[300^{\text{°}} - 360^{\text{°}} = -60^{\text{°}} \]
Subtract another 360 degrees:

• From -60 degrees:

\[ -60^{\text{°}} - 360^{\text{°}} = -420^{\text{°}} \]
By subtracting multiples of 360 degrees, you maintain the coterminal nature of the angles but shift into the negative domain. This technique is helpful for periodic phenomena and waveform analyses.