For each of the following angles, find a coterminal angle with measure (theta symbol) such that 0 degrees is greater than or equal to omega symbol < 360 degrees.
a) -100 degrees.
I really do not understand how to work this problem and I need help.
Generally angles are expressed as values between 0 and 360 degrees.
Since there are 360 degrees in a circle, adding or subtracting 360 from the value will not change the terminal point of the angle. It just means you have done an extra clockwise or counter-clockwise rotation about the origin.
So, -100° represents the same angle as all of the following:
... -820° -460° -100° 260° 620° ...
so, which of those values is between 0° and 360°?
To find a coterminal angle with measure -100 degrees within the range of 0 degrees to 360 degrees, you can add or subtract an integer multiple of 360 degrees to -100 degrees.
To find a positive coterminal angle, add 360 degrees:
-100 degrees + 360 degrees = 260 degrees
To find a negative coterminal angle, subtract 360 degrees:
-100 degrees - 360 degrees = -460 degrees
However, since we want an angle within the range of 0 to 360 degrees, we need to find the coterminal angle by adding or subtracting an integer multiple of 360 degrees that brings us within this range.
Adding 360 degrees once again:
-460 degrees + 360 degrees = -100 degrees
Therefore, the coterminal angle with measure -100 degrees within the range of 0 degrees to 360 degrees is -100 degrees.
To find a coterminal angle with a given angle measure, you need to add or subtract a multiple of 360 degrees until you get an angle that satisfies the condition of being between 0 and 360 degrees.
For the given angle, which is -100 degrees, you can add 360 degrees to it:
-100 degrees + 360 degrees = 260 degrees
So, 260 degrees is a coterminal angle with -100 degrees that satisfies the condition.