1. ## unit circle

Hi;
how do I find the coordinates for points on the unit circle knowing just its degree in radians ie what the coordinates for 26/45pi = 104degree.

Thanks.

2. ## Re: unit circle

Assuming the standard coordinate system where 0 radians corresponds to the x-axis we have for a point $(x,y)$ on the unit circle

$(x,y) = (\cos(\theta), \sin(\theta))$

3. ## Re: unit circle

thanks but I only know the radius=1 and one angle=90, I don't know the length of x or y

4. ## Re: unit circle

Originally Posted by anthonye
thanks but I only know the radius=1 and one angle=90, I don't know the length of x or y
what do you mean you only know one angle? The formula I wrote lets you solve for $(x,y)$ given only the angular displacement $\theta$

5. ## Re: unit circle

Originally Posted by anthonye
how do I find the coordinates for points on the unit circle knowing just its degree in radians ie what the coordinates for 26/45pi = 104degree.
Originally Posted by anthonye
thanks but I only know the radius=1 and one angle=90, I don't know the length of x or y
From what you posted the answers are: $x = \cos \left( {\frac{{26\pi }}{{45}}} \right)\,\& \,y = \sin \left( {\frac{{26\pi }}{{45}}} \right)$.

6. ## Re: unit circle

when I enter cos(104) I get -0.2419...but when I enter cos(26pi/45) I get 0.999 What an I doing wrong?

Thanks.

7. ## Re: unit circle

Originally Posted by anthonye
when I enter cos(104) I get -0.2419...but when I enter cos(26pi/45) I get 0.999 What an I doing wrong?
I would say that you don't know how to use your own calculator.
Look at this website.

BTW, degrees are really obsolete for most mathematics courses.

8. ## Re: unit circle

can you just tell me which one is right then I can work from there?

9. ## Re: unit circle

Originally Posted by anthonye
can you just tell me which one is right then I can work from there?
Your calculator is set to input angles in degrees. You'll have to change that to radians to input $\dfrac{26 \pi}{45}$ correctly.

The correct answer is $\cos\left(\dfrac{26\pi}{45}\right) \approx -.2419$

10. ## Re: unit circle

You have your calculator set to degrees. So $\cos(104^\circ)$ is correct. $\cos\left(\dfrac{26\pi}{45}^\circ\right)$ is not correct. $\cos(104^\circ) = \cos\left(\dfrac{26\pi}{45}\right)$ (Notice the lack of a degree symbol on the RHS of the equation, because the RHS is in radians rather than degrees).

11. ## Re: unit circle

Thank you for all your help