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Math Help - express in m and n

  1. #1
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    Exclamation express in m and n

    If cos θ = m^2-n^2 / m^2+n^2 , where m>n>0,and cosec θ <0 , express sin θ and tan θ in terms of m and n.
    i don't really know how to even start it.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hint(I think):

    sin^2(x)+cos^2(x)=1
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  3. #3
    Member Mathelogician's Avatar
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    Use the identity sin^2(x)+cos^2(x)=1 and the definition of tangent.
    Just note that cos(x)>0 (why?)
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  4. #4
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    Quote Originally Posted by Mathelogician View Post
    Use the identity sin^2(x)+cos^2(x)=1 and the definition of tangent.
    Just note that cos(x)>0 (why?)
    emm can u explain how to use that identity.as so far i learned i didn't learned this identity,but when i fliped to the later part of the chpt,i saw it.
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  5. #5
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    Hello, tempq1!

    \text{If }\:\cos\theta \,=\, \dfrac{m^2-n^2}{m^2+n^2}\:\text{ where } m>n>0\:\text{ and }\:\csc\theta < 0

    . . \text{express }\sin\theta\text{ and }\tan\theta\text{ in terms of }m\text{ and }n.

    \text}We are given: }\;\cos\theta \:=\:\dfrac{m^2-n^2}{m^2+n^2} \;=\;\dfrac{adj}{hyp}


    \cs\theta is in a right triangle with: . adj \,=\, m^2-n^2,\;hyp \,=\, m^2+n^2

    Using Pythagorus, we find that: . opp \,=\,\pm 2mn

    And we can now express \sin\theta and \tan\theta.


    To apply the correct signs to our answer, we note that:

    . . \cos\theta is positive: \cs\theta is in Quadrant 1 or 4.

    . . \csc\theta is negative: \cs\theta is in Quadrant 3 or 4.

    . . . . Hence, \cs\theta is in Quadrant 4.


    Go for it!

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  6. #6
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    Quote Originally Posted by Soroban View Post
    Hello, tempq1!


    \text}We are given: }\;\cos\theta \:=\:\dfrac{m^2-n^2}{m^2+n^2} \;=\;\dfrac{adj}{hyp}


    \cs\theta is in a right triangle with: . adj \,=\, m^2-n^2,\;hyp \,=\, m^2+n^2

    Using Pythagorus, we find that: . opp \,=\,\pm 2mn

    And we can now express \sin\theta and \tan\theta.


    To apply the correct signs to our answer, we note that:

    . . \cos\theta is positive: \cs\theta is in Quadrant 1 or 4.

    . . \csc\theta is negative: \cs\theta is in Quadrant 3 or 4.

    . . . . Hence, \cs\theta is in Quadrant 4.


    Go for it!


    oh ya my teacher taught me how to do the next day already.thanks anyway.i understand how to do already.
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