Question 1064458: What is the reference angle for an angle with a measure of -405 degrees?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the angle is -405 degrees.
the reference angle would be the equivalent angle in the first quadrant.
keep adding 360 to the angle until it becomes positive and is between 0 and 360 degrees.
-405 + 360 = -45 degrees.
-45 degrees + 360 = 315 degrees.
that's the equivalent positive angle that is between 0 and 360 degrees.
that angle is in the fourth quadrant.
the equivalent angle in the first quadrant is equal to 360 - 315 degrees which is equal to 45 degrees.
if you knew that a negative angle in the fourth quadrant is the same as a positive angle in the first quadrant, you could have just said that, since the angle is -45 in the fourth quadrant, then it has to be 45 degrees in the first quadrant.
if you didn't know that, then the procedure described above will get you the correct answer.
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