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Math Help - Trigonometric identites

  1. #1
    Member smmmc's Avatar
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    Trigonometric identites

    Hey this question above.

    my working out

    tan theta= 1/cot theta = cos theta/ sin theta
    tan theta= cos ( -7/24) / sin(-7/24)

    cos theta=0.957766
    sin theta= -0.287549 or 0.29

    the back of the book says
    cos theta - 24/25, thats correct
    but sin theta=-7/25 which equals -0.28

    help?

    thanks
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  2. #2
    Member smmmc's Avatar
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    And this

    my working out 1 + tan^2theta = sec^2theta
    squareroot 1.16 = sec theta
    sec theta= 1.07703

    how do i find when its neg of pos?

    thank you again
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  3. #3
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    Quote Originally Posted by smmmc View Post
    Hey this question above.

    my working out

    tan theta= 1/cot theta = cos theta/ sin theta
    tan theta= cos ( -7/24) / sin(-7/24)

    cos theta=0.957766
    sin theta= -0.287549 or 0.29

    the back of the book says
    cos theta - 24/25, thats correct
    but sin theta=-7/25 which equals -0.28

    help?

    thanks
    \tan{\theta} = -\frac{7}{24} = \frac{opposite}{adjacent}

    sketch a reference triangle in quad IV ... hypotenuse = 25

    \sin{\theta} = \frac{opposite}{hypotenuse} = -\frac{7}{25}

    \cos{\theta} = \frac{adjacent}{hypotenuse} = \frac{24}{25}
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  4. #4
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    Quote Originally Posted by smmmc View Post
    And this

    my working out 1 + tan^2theta = sec^2theta
    squareroot 1.16 = sec theta
    sec theta= 1.07703

    how do i find when its neg of pos?

    thank you again
    \tan{\theta} = 0.4 > 0 ... \theta is in quad III, so \sec{\theta} < 0

    \sec{\theta} = -\sqrt{1 + \tan^2{\theta}}
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