# It says convert (-1, pi/8 ) from polar to rectangular coordinate?

How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular?
It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle?
If the'yre on the unit circle just use x=rcosθ and y=rcosθ
another example is for (1, 5pi/2) That doesn't seem to be on the unit circle either. So how can we do these then?

## Answers and Replies

Dick
Science Advisor
Homework Helper
How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular?
It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle?
If the'yre on the unit circle just use x=rcosθ and y=rcosθ
another example is for (1, 5pi/2) That doesn't seem to be on the unit circle either. So how can we do these then?

-1 is your r and pi/8 is your theta. Like you said use x=rcosθ and y=rcosθ.

-1 is your r and pi/8 is your theta. Like you said use x=rcosθ and y=rcosθ.

YOU CAN'T
it won't work unless they're on the unit circle

Dick
Science Advisor
Homework Helper
YOU CAN'T
it won't work unless they're on the unit circle

"polar coordinates" means the ordered pair is (r,theta). You want to convert that to (x,y). As long as |r|=1 it is on the unit circle.

"polar coordinates" means the ordered pair is (r,theta). You want to convert that to (x,y). As long as |r|=1 it is on the unit circle.

OK how, you keep saying you can do it, so please do, because that's what I'm asking. do it do it do it lol please haha

p.s. the 5pi/2 that's just where pi/2 is, but the pi/8 WHERE is that?

eumyang
Homework Helper
YOU CAN'T
it won't work unless they're on the unit circle

Are you saying that since π/8 is not one of the special angles (those related to 30°, 45°, and 60°), the angle is not "on the unit circle"? If that is the case, so what? Either use a calculator to evaluate the necessary trig functions of π/8, or use a trig identity.

For example, if the point is (1, 105°), then in rectangular coordinates it's (cos 105°, sin 105°). Use a calculator and you get (-0.259, 0.966). Or use the fact that 105° = 60° + 45° and evaluate cos (60° + 45°) and sin (60° + 45°). That's it!