Find the measure of an angle between 0 degrees and 360 degrees coterminal with a -120-degrees angle.
A 240-degree angle is coterminal with a -120-degree angle because -120 + 240 = 120, which is a full revolution. Thus, an angle between 0 degrees and 360 degrees coterminal with a -120-degree angle is 240 degrees.
" .... because -120 + 240 = 120 " has nothing to do with the problem.
You are correct. I apologize for the mistake in my previous response.
To find an angle between 0 degrees and 360 degrees that is coterminal with -120 degrees, we can add 360 degrees (a full revolution) to -120 degrees until we get an angle that falls between 0 and 360 degrees.
-120 + 360 = 240
So, 240 degrees is an angle between 0 and 360 degrees that is coterminal with -120 degrees.
That's better
Thank you for bringing it to my attention. I always strive to provide accurate responses.
To find the measure of an angle that is coterminal with a given angle, you can simply add or subtract a multiple of 360 degrees.
Given that the angle is -120 degrees, the coterminal angle between 0 degrees and 360 degrees can be found by adding a multiple of 360 degrees to -120 degrees.
To find the positive coterminal angle, add 360 degrees to -120 degrees:
-120 degrees + 360 degrees = 240 degrees
Therefore, the measure of an angle between 0 degrees and 360 degrees coterminal with -120 degrees is 240 degrees.
To find the measure of an angle coterminal with a given angle, you can simply add or subtract multiples of 360 degrees until you get an angle within the desired range.
Given that the angle is -120 degrees, we can find a coterminal angle as follows:
1. Subtract multiples of 360 degrees from the given angle until we get an angle between 0 and 360 degrees.
-120 degrees - 360 degrees = -480 degrees (outside the desired range)
-120 degrees - 2(360 degrees) = -840 degrees (outside the desired range)
-120 degrees - 3(360 degrees) = -120 degrees (within the desired range)
Therefore, a coterminal angle between 0 and 360 degrees with -120 degrees is -120 degrees.