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Math Help - Not sure about this trig question

  1. #1
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    Not sure about this trig question

    Sorry for the vague title, but I'm not sure what to call it.



    I have a series of questions based on the above figure, but I'm not sure how to look at it. It asks to state the value of certain trigonometric ratios.

    First one is Sin \theta, and the answer in the back of the book is b. I'm not sure how they got just b as I would have thought it to be \displaystyle \frac{y}{r} for sin.

    If anyone could help me read the figure/answer one of the questions so I could finish it off, I would greatly appreciate it!
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  2. #2
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    as I would have thought it to be \displaystyle \frac{y}{r} for sin.
    That is absolutely correct.
    But also notice that r=1, look at the diagram.
    \displaystyle \frac{b}{1}=b
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  3. #3
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    Quote Originally Posted by Plato View Post
    That is absolutely correct.
    But also notice that r=1, look at the diagram.
    \displaystyle \frac{b}{1}=b
    How do you know r=1?
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  4. #4
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    Quote Originally Posted by IanCarney View Post
    How do you know r=1?
    Look at the diagram.
    That is the unit circle.
    Center at (0,0) and contains the point (1,0).
    So the radius is r=1.
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  5. #5
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    Quote Originally Posted by Plato View Post
    Look at the diagram.
    That is the unit circle.
    Center at (0,0) and contains the point (1,0).
    So the radius is r=1.
    But I thought we were using the point (a,b) and not (1,0)? Or does that not matter (I assumed that the radius would be different)?
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  6. #6
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    Quote Originally Posted by IanCarney View Post
    But I thought we were using the point (a,b) and not (1,0)? Or does that not matter (I assumed that the radius would be different)?
    A circle is a set of points that are all equally distant, the radius, from a fixed point, the center. So every point on that circle is one unit from (0,0).

    Thus r^2=a^2+b^2=1~!
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