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Math Help - Another Unit circle question

  1. #1
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    Another Unit circle question

    Can someone explain me these using the unit circle?

    cos(180-theta)= -cos theta
    cos(-theta)=cos theta
    sin(-theta)= -sin theta

    Thanks!
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  2. #2
    Senior Member sakonpure6's Avatar
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    Re: Another Unit circle question

    Hello laurettarosa! Are you familiar with the C.A.S.T Rule? Basically, it helps us determine where the trig ratios: sin, cos, and tan are positive or negative.
    Let Q = theta.
    Another Unit circle question-7-3.jpg

    The C in CAST is located in the 4th quadrant, and only Cosine is positive there.
    The A in CAST is located in the 1st quadrant and Sine, Cosine, and Tan are positive there.
    The S in CAST is located in the 2nd quadrant and only Sine is positive there
    The T is CAST is located in the 3rd quadrant and only Tan is positive there.

    Moving on,

    cos(180 - Q) : Analysing the angle: 180 - Q, this means that Q is located in the 2nd quadrant and according to CAST, only sine is positive there.
    Therefore, cos(180 - Q) = - cos Q

    Can you handle the rest? if you have any other questions, please do not hesitate to ask.
    Last edited by sakonpure6; February 9th 2014 at 02:17 PM.
    Thanks from laurettarosa
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  3. #3
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    Re: Another Unit circle question

    Quote Originally Posted by laurettarosa View Post
    Can someone explain me these using the unit circle?

    cos(180-theta)= -cos theta
    cos(-theta)=cos theta
    sin(-theta)= -sin theta

    Thanks!
    for the first one just look at the picture I made for you. What happens to the x coordinate after you flip it about the y axis.

    for the next two it's the same idea but you are flipping it w/respect to the x axis.

    Draw a picture like the one I drew for you.
    Thanks from laurettarosa
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