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Math Help - Coterminal Angles

  1. #1
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    Coterminal Angles

    I am having trouble understanding coterminal angles.

    For the next set of questions, I need to find two angles coterminal with:

    (a) 107pi/18

    (b) 60 degrees

    (c) -30 degrees

    I don't just want answers. I need an explanation.

    Thank you
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  2. #2
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    Quote Originally Posted by magentarita View Post
    I am having trouble understanding coterminal angles.

    For the next set of questions, I need to find two angles coterminal with:

    (a) 107pi/18

    (b) 60 degrees

    (c) -30 degrees

    I don't just want answers. I need an explanation.

    Thank you
    Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof. Check this site for further info:
    Mathwords: Coterminal Angles

    To do the problems above, just add 360 degrees/2π radians to the original angle, and subtract 360 degrees/2π radians from the original angle. For (a) this would be
    \frac{107\pi}{18} + 2\pi = \frac{107\pi}{18} + \frac{36\pi}{18} = \frac{143\pi}{18} and
    \frac{107\pi}{18} - 2\pi = \frac{107\pi}{18} - \frac{36\pi}{18} = \frac{71\pi}{18} .

    What you add/subtract is arbitrary, since the directions didn't specify. I could have taken the original angle and added 720 degrees and 1080 degrees and those answers would also be valid. In other words, there are a whole lot of angles that are coterminal with each other.


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  3. #3
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    good but...

    I understood everything you said except the following:

    "Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof."

    Can you give me an example of "multiples thereof"?

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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by magentarita View Post
    I understood everything you said except the following:

    "Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof."

    Can you give me an example of "multiples thereof"?
    do you know that

    \pi=180^o

    so when add [tex]2\pi[tex] it is the same as when you add 360^o

    multiples thereof :

    example
    \frac{\pi}{3}=\frac{\pi}{3}+2\pi=\frac{\pi}{3}+4\p  i.....

    in degrees

    75^o=75^o+360^o=75^o+2(360^o)=75^o-360^o.....

    so for any angle in rad or in degree

    \theta=\theta\pm2n\pi......\forall n\in R

    angle in degree let me call it phi

    \phi=\phi\pm n(360^o)....\forall n\in R
    Last edited by Amer; June 4th 2009 at 05:06 AM.
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  5. #5
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    Quote Originally Posted by magentarita View Post
    I understood everything you said except the following:

    "Coterminal angles in the Cartesian plane have the same initial side and terminal side; the difference is that they can be obtained by adding or subtracting 360 degrees/2π radians, or multiples thereof."

    Can you give me an example of "multiples thereof"?
    Hi magentarita,

    Look at it this way. Let's say you have a 30 degree angle, initial side on the positive x-axis, terminal side in the 1st quadrant. If you add 360, you obtain a coterminal angle of 390. Multiples thereof would indicate that 30 + any multiple of 360 would also produce an angle coterminal with 30 degrees.

    30 + {\color {red}1}(\pm360) = 390 \ \ or \ \ -330

    30 + {\color{red}2}(\pm360) = 750 \ \ or \ \ -690
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