Which quadrant does the terminal side of -290 degrees lie?

1 Answer
Noah G
Jul 20, 2016

First of all, its always easier to work with positive angles. Recall that in the unit circle, there are #360˚#.

When an angle is positive, it goes counterclockwise from the origin.

When an angle is negative, it goes clockwise from the origin.

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So, #sin(-96)˚ = sin(264)# and #sin96˚ = sin(-264)#. The only difference is that they went opposite directions. Hence, their terminal arms will be in the same quadrant.

Let your angle be #x#:

#x_"positive" = 360 - 290#

#x_"positive" = 70˚#

Thus, #-290˚ = 70˚# The following shows the allotment of the angles, by quadrant:

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Our angle of #70˚#, assuming it's #x#, is located between #0˚# and #90˚#, or in quadrant 1.

Hopefully this helps!

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