Tori Hines

2022-01-23

Where is the angle for $-\frac{7\pi }{8}$ in a unit circle?
I am having difficulty finding the angle for $-\frac{7\pi }{8}$ in a unit circle. I have found the coordinates for $\frac{\pi }{8}$ and have to use the symmetry to locate the coordinates for $-\frac{7\pi }{8}$. Is the angle just below the (1,0) and symmetry to $\frac{\pi }{8}$?

Flickkorbma

Expert

$-\frac{7\pi }{8}=\frac{\pi }{8}-\pi$ . So you must rotate your point clockwise through an angle $\pi$. This will take you to a point directly opposite the point you started from.

oferenteoo

Expert

$-\frac{7\pi }{8}$ is in the third quadrant. So, using $\frac{\pi }{8}$ as your reference angle, make both coordinates negative.
(It is also coterminal with $\frac{9\pi }{8}$, since they differ by $2\pi$.)

Do you have a similar question?