SOLUTION: I learned about coterminal angles, but I have some questions: When you calculate the coterminal angle of -240° you get 120° as an answer (being the lowest positive coterminal

Question 1199545: I learned about coterminal angles, but I have some questions:
When you calculate the coterminal angle of -240° you get 120° as an answer (being the lowest positive coterminal angle). However, when you do -240 - 360 you get -600° (which is a negative coterminal angle) but not the lowest negative coterminal angle. The lowest negative coterminal angle is -240°. Why is the lowest negative coterminal angle -240° and not -600°?

Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

You seem to have some misconceptions about coterminal angles.

Given the measure of an angle, there are an infinite number of coterminal angles -- found by adding or subtracting any multiple of 360 degrees to the measure of the given angle.

So it is incorrect (or, at least, nonstandard) terminology to talk about "THE" coterminal angle of a given angle.

With your given angle of -240 degrees, ONE coterminal angle is -240+360 = 120 degrees. But other coterminal angles are -240-360 = -600 degrees, or -240-720 = -960 degrees, or -240+1080 = 840 degrees, or an infinite number of others.

In many instances, it makes sense to view an angle between 0 and 360 degrees as the "primary" coterminal angle, so in your case the "primary" coterminal angle is 120 degrees.

I have never seen a reference that talks about the "lowest negative coterminal angle". Apparently the reference you are using calls the coterminal angle between 0 and -360 degrees the lowest negative coterminal angle; since the given angle -240 degrees is already in that range, it is the lowest negative coterminal angle.

I hope that helps....

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