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

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.

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 $x$:

${x}_{\text{positive}} = 360 - 290$

x_"positive" = 70˚

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

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

Hopefully this helps!