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Thread: 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 $\displaystyle Sin \theta$, and the answer in the back of the book is $\displaystyle b$. I'm not sure how they got just $\displaystyle b$ as I would have thought it to be $\displaystyle \displaystyle \frac{y}{r}$ 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 $\displaystyle \displaystyle \frac{y}{r}$ for sin.
    That is absolutely correct.
    But also notice that $\displaystyle r=1$, look at the diagram.
    $\displaystyle \displaystyle \frac{b}{1}=b$
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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 $\displaystyle r=1$, look at the diagram.
    $\displaystyle \displaystyle \frac{b}{1}=b$
    How do you know $\displaystyle r=1$?
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  4. #4
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    Quote Originally Posted by IanCarney View Post
    How do you know $\displaystyle r=1$?
    Look at the diagram.
    That is the unit circle.
    Center at $\displaystyle (0,0)$ and contains the point $\displaystyle (1,0)$.
    So the radius is $\displaystyle r=1$.
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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 $\displaystyle (0,0)$ and contains the point $\displaystyle (1,0)$.
    So the radius is $\displaystyle r=1$.
    But I thought we were using the point $\displaystyle (a,b)$ and not $\displaystyle (1,0)$? 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 $\displaystyle (a,b)$ and not $\displaystyle (1,0)$? 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 $\displaystyle (0,0)$.

    Thus $\displaystyle r^2=a^2+b^2=1~!$
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