Question

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

Answer 1

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_"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!