Question

Find the reference angle for the given angle. Show work

Answer 1

Answer: 44 degrees

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Since the given angle -404 is not between 0 and 360, we add 360 to it to get:
-404 + 360 = -44

We add another 360 to that result
-44 + 360 = 316
now we have a value between 0 and 360

Rules:
* If the angle is between 0 and 90, we stop here and simply write down that value

* If the angle x is between 90 and 180, then we compute 180-x

* If the angle x is between 180 and 270, then we compute x-180

* If the angle x is between 270 and 360, then we compute 360-x

* Note in the three rules above, the order of subtraction is always (larger angle)-(smaller angle) = reference angle

* The reference angle has one segment on the x axis (aka the reference angle is adjacent to the x axis)

Based on that, we see that 316 is between 270 and 360, so we use the rule that
360-x
In this case, x = 316

So,
360-x = 360-316 = 44

The reference angle is 44 degrees and looks like what you see in the attached image.

Answer 2

If the angle is negative, then it is rotated clockwise. The angle -404 degrees has rotated morethan 1 cycle or 360 degrees.

-404 + 360 = -44 degrees. The reference angle will always be the angle with respect to the x - axis. 

-44 degrees is from the origin or the 0 degrees rotated clockwise to the -44degrees. 

The reference angle is 44 degrees