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Math Help - angles help. sin0.5x

  1. #1
    Member helloying's Avatar
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    angles help. sin0.5x

    Given that x is an obtuse angle and sin x =3/5, find, without the use of calculator, cos0.5x

    please help me thanks. Also, i have something to clarify,in cases like this:  2\sin x\cos x  = 3\cos^2 xsolve for x between 0 to 180 deg
    can i just cancel out cos x ? then i will have tan x =3/2 x=56.3

    but since i cancel out the cos x so it is suppose to be zero so i just put cos x =0 and x=90

    the zero part doesnt sound very logical to me.is it right to do that?
    Last edited by helloying; June 22nd 2009 at 07:29 AM.
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  2. #2
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    Quote Originally Posted by helloying View Post
    Given that x is an obtuse angle and sin x =3/5, find, with the use of calculator, cos0.5x

    please help me thanks. Also, i have something to clarify,in cases like this:  2\sin x\cos x = 3\cos^2 xsolve for x between 0 to 180 deg
    can i just cancel out cos x ? then i will have tan x =3/2 x=56.3

    but since i cancel out the cos x so it is suppose to be zero so i just put cos x =0 and x=90

    the zero part doesnt sound very logical to me.is it right to do that?

    (1)sin x =3/5 (x is in quadrant 2)

    x=143.13 degree

    Then use the calculator to find cos 0.5(143.13)

    (2)  2\sin x\cos x = 3\cos^2 x

    No u cannot cancel like that .

    3cos^2x-2sinxcosx=0

    cosx(3cosx-2sinx)=0

    cosx=0 , x = ..

    3cosx=2sinx

    3/2=tanx , x=..
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  3. #3
    Member helloying's Avatar
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    Quote Originally Posted by mathaddict View Post
    (1)sin x =3/5 (x is in quadrant 2)

    x=143.13 degree

    Then use the calculator to find cos 0.5(143.13)

    (2)  2\sin x\cos x = 3\cos^2 x

    No u cannot cancel like that .

    3cos^2x-2sinxcosx=0

    cosx(3cosx-2sinx)=0

    cosx=0 , x = ..

    3cosx=2sinx

    3/2=tanx , x=..

    thank you very much for ur reply but i am sorry, for the 1st part i have asked for how to solve it without the use of calculator.i have typed wrongly . i corrected my mistake now.
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  4. #4
    Member great_math's Avatar
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    Quote Originally Posted by helloying View Post
    Given that x is an obtuse angle and sin x =3/5, find, without the use of calculator, cos0.5x

    please help me thanks. Also, i have something to clarify,in cases like this:  2\sin x\cos x  = 3\cos^2 xsolve for x between 0 to 180 deg
    can i just cancel out cos x ? then i will have tan x =3/2 x=56.3

    but since i cancel out the cos x so it is suppose to be zero so i just put cos x =0 and x=90

    the zero part doesnt sound very logical to me.is it right to do that?
    sin x=3/5 so \cos x=\frac{-4}{5}

    Now, \cos2\theta=2\cos^2\theta-1

    \cos(2\times0.5x)=2\cos^20.5x-1

    \Rightarrow \cos x+1=2\cos^20.5x

    \Rightarrow \frac1{5}=2\cos^20.5x

    \Rightarrow \cos^20.5x=\frac1{10}

    \Rightarrow \cos 0.5x=\frac{1}{\sqrt{10}}

    \Rightarrow \cos 0.5x\approx\frac1{3.16}\approx 0.31
    Last edited by great_math; June 22nd 2009 at 07:50 AM.
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  5. #5
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    Quote Originally Posted by helloying View Post
    thank you very much for ur reply but i am sorry, for the 1st part i have asked for how to solve it without the use of calculator.i have typed wrongly . i corrected my mistake now.
    i felt really awkward when u said with the calculator .. btw without the calculator , you will need to use the half angle formula .

    From the double angle formula :

    cos 2a = 2cos^2a-1

    Let a =x/2

    cos x= 2cos^2(x/2)-1

    (cosx+1)/2=cos^2(x/2)

     <br />
cos(\frac{x}{2})=\pm\sqrt{\frac{cosx+1}{2}}<br />

    Now , find cos\frac{1}{2}x

    substitute x=143.13 and take the positive value .
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