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Thread: unit circle

  1. #1
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    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.
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  2. #2
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    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

    $(x,y) = (\cos(\theta), \sin(\theta))$
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  3. #3
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    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
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    Re: unit circle

    Quote Originally Posted by anthonye View Post
    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 $\theta$
    Thanks from anthonye
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  5. #5
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    Re: unit circle

    Quote Originally Posted by anthonye View Post
    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.
    Quote Originally Posted by anthonye View Post
    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: $x = \cos \left( {\frac{{26\pi }}{{45}}} \right)\,\& \,y = \sin \left( {\frac{{26\pi }}{{45}}} \right)$.
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  6. #6
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    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?

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  7. #7
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    Re: unit circle

    Quote Originally Posted by anthonye View Post
    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.
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  8. #8
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    Re: unit circle

    can you just tell me which one is right then I can work from there?
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    Re: unit circle

    Quote Originally Posted by anthonye View Post
    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 $\cos\left(\dfrac{26\pi}{45}\right) \approx -.2419$
    Thanks from anthonye
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  10. #10
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    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).
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    Re: unit circle

    Thank you for all your help
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  12. #12
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    Re: unit circle

    romsek gave the best answer.

    But, from the unit circle, you could also plug in your radius vector 1 and your given angle 104-deg into your calc's polar-to-rectangular conversion feature:

    P>Rx(1,104) = -0.24
    P>Ry(1,104) = 0.97

    unit circle-geo-robot.png
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