What is the reference angle for -140 degrees?

Answer 1

in order to find the reference angle, an angle less than or equal to 90 degrees formed by the x-axis and the terminal side of an angle, one needs to first find what quadrant on the coordinate plane the angle belongs to.

The negative (-) sign in -140 refers to the direction 360 degree turn begins at (and therefore the quadrant it begins at). Instead of taking the regular backwards "C", counterclockwise direction, the turn begins clockwise. To convert it, simply add 360 degrees, to get 220 degrees, an angle in the third quadrant.

These are the guidelines to follow when finding reference angles:

If angle, A, is in first quadrant then the reference angle will be itself as it is already 90 degrees or under.

If angle, A, is in second quadrant then the reference angle will be 180 - A .

If angle, A, is in third quadrant then the reference angle will be A - 180 .

If angle, A, is in fourth quadrant then the reference angle will be 360 - A "

These subtractions are all in reference to the nearest angle of a quadrant and are in degrees.

Being in the third quadrant, take the angle, A, and subtract 180 from it to get:

220 - 180 = 40

Thus, the reference angle for -140 degrees is 40 degrees.

Follow the same directions for other angles, first determining whether the angle needs to be converted into a positive value (counterclockwise), then locate the quadrant and use the rules above for the specific angle(s) being looked at and asked for.