Question

What are the coordinates of the point that corresponds to -7π/4 on the unit circle

Answer 1

Take a look at the attached picture of the unit circle.

If you have negative radians, you would go around the circle counterclockwise starting from 0. Remember that 1π is a semicircle. Go counterclockwise 1π to get to 180° or (-1,0).

Now you just need to go counterclockwise 3π/4 more, since 7π/4 is 3π/4 more than π. 3/4 of π would just be 3/4 of a semicircle. (Try to imagine that in your head. It looks like 3 slices of a pizza that was cut into 8 slices.) The second picture shows you moving 3π/4 from π on the unit circle, which would put you at 45° or π/4.

At π/4, the coordinates are $(\frac{ \sqrt{2} }{2} , \frac{ \sqrt{2} }{2} )$.

--------

Answer: $(\frac{ \sqrt{2} }{2} , \frac{ \sqrt{2} }{2} )$