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Math Help - Cosine/Sine

  1. #1
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    Cosine/Sine

    Find the value of cos(theta) if sin(theta)=8/17 and cos(theta)<0.

    I cannot seem to get the right answer but here is what I did.

    Cos= adjacent/ hypoteneuse
    Sin= Opposite/ hypoteneuse

    Now I drew a right trible and labeled the angle with respect to theta. So the hypotenese was 17 and the base was 15. Now to find the right side of the triangle I applied Pathyogreans theorm (I can't spell) and set it up like this:

    8^2+B^2=17^2 ; solved for b and 15.

    According to me Cosine, which I am looking for should be (15/17) but somehow when I am typing the information back into the comuter system it wont accept the answer, what am I doing wrong?

    Thanks
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  2. #2
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    Hello, qbkr21!

    Find the value of \cos\theta if \sin\theta = \frac{8}{17} and \cos\theta < 0

    Here is what I did.
    \cos =  \frac{adj}{hyp}\quad\sin =  \frac{opp}{hyp}

    Now I drew a right triangle and labeled the angle with respect to \theta.
    So the hypotenese was 17 and opp was 15.
    Now to find the adj side of the triangle I applied Pythagorus' theorem

    and set it up like this: . 8^2 + b^2\:=\:17^2 solved for b = 15
    here!

    According to me, cosine should be \frac{15}{17}, but the computer won't accept the answer.

    You overlooked one of the conditions: . \cos\theta < 0
    . . If \cos\theta is negative, then \theta is in Quadrant 2 or 3.

    Since \sin\theta is positive, \theta is in Quadrant 1 or 2.
    . . Hence, \theta is in Quadrant 2.

    Your triangle should look like this:
    Code:
            *       |
            | \  17 |
           8|   \   |
            |     \ θ
          - + - - - + - -
                b   |

    Be very careful when using Pythagorus . . .

    You had: . 8^2 + b^2\:=\:17^2\quad\Rightarrow\quad b^2\:=\:225

    . . Then: . b = 15

    And you must choose the correct sign, you see.

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  3. #3
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    Re:

    Sir I am still confused. The system won't take the following answers I tried: -15,15, or (15/17). I am still missing a couple of pieces to this puzzle can you help me a little further?

    Thanks
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  4. #4
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    Re:

    YES YES YES!! I got it right, that numonic device just hit me: ALL STUDENTS TAKE CALCULUS.

    A: (-15/17)
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