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Math Help - more trig

  1. #1
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    more trig

    1. show that cos150/sin150=1/tan150

    2. prove tan O cos O = sin O
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by william View Post
    1. show that cos150/sin150=1/tan150

    2. prove tan O cos O = sin O
    Hint: \cot\vartheta=\frac{\cos\vartheta}{\sin\vartheta} and \tan\vartheta=\frac{\sin\vartheta}{\cos\vartheta}.

    Do you think you can do these now?
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    Hint: \cot\vartheta=\frac{\cos\vartheta}{\sin\vartheta} and \tan\vartheta=\frac{\sin\vartheta}{\cos\vartheta}.

    Do you think you can do these now?
    can you be a bit more specific i am not sure exactly what you mean
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  4. #4
    Senior Member euclid2's Avatar
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    Quote Originally Posted by william View Post
    1. show that cos150/sin150=1/tan150

    2. prove tan O cos O = sin O
    2.
    Prove that tan\vartheta   cos\vartheta = sin \vartheta

    =tan\vartheta cos\vartheta = sin \vartheta

    =(sin\vartheta/cos\vartheta)cos\vartheta

    =sin \vartheta
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  5. #5
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    Being more specific is like providing the answer for this particular question but nevertheless hope you will be able to learn from the answer and solve future proving problems.

    tan O cos O = sin O

    From L.H.S
    (sin O/cos O) cos O
    sin O (proven)

    Quote Originally Posted by william View Post
    can you be a bit more specific i am not sure exactly what you mean
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  6. #6
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    For the first question,

    cos150/sin150=1/tan150

    From R.H.S

    1/tan150 = ( 1/sin150/cos150 )
    1/sin150/cos150 = 1 x cos150/sin150
    = cos150/sin150 (proven)

    For proving question try to have a formula sheet which contains all the trigo identities and ask yourself a few qns like what trigo identity can i use to solve the problem. You will be able to solve problem fairly easily with constant practice. Hope it helps.
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  7. #7
    Senior Member euclid2's Avatar
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    Quote Originally Posted by william View Post
    1. show that cos150/sin150=1/tan150

    2. prove tan O cos O = sin O
    1. cos150/sin150=1/tan150

    sketch the angle in standard position. Then determine the values of x,y,r,using the 30 deg triangle and that it lies in the quadrant 2.

    from the diagram, i can see that
    1.cos150=-sqrt3/2
    2.sin150=1/2
    3.tan150=-1/sqrt3

    therefore: cos150/sin150=1/tan150
    =-sqrt3/2over1/2 = 1/1/-sqrt3
    =(-sqrt3/2)(2/1)=1*-sqrt3/1
    =-sqrt3=-sqrt3

    therefore: cos150/sin150=1/tan150
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