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Math Help - trig equation

  1. #1
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    Talking trig equation

    1) cos(40+x)=3sin(50+x) find x for 0<x<360 in degrees

    2) 8sinxcosx=3 solve x for 0<x<2pi answer in radians

    thanks!
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  2. #2
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    1. cos(a+b) = cos a cos b - sin a sin b and sin(a+b) = sin a cos b + sin b cos a so cos(40+x) = cos 40 cos x - sin 40 sin x and sin(50+x) = sin 50 cos x + cos 50 sin x. The result is cos 40 cos x - sin 40 sin x = 3 sin 50 cos x + 3 cos 50 sin x

    cos 40 cos x - sin 40 sin x = 3 cos 40 cos x + 3 sin 40 sin x

    2 cos 40 cos x + 4 sin 40 sin x = 0; 4 sin 40 sin x = -2 cos 40 cos x

    \frac{-cos 40}{2 sin 40} = \frac{sin x}{cos x}

    tan x = \frac{-cos 40}{2 sin 40}

    x = arctan{\frac{-cos 40}{2 sin 40}}

    2. 8 sin x cos x = 4 sin 2x = 3

    sin 2x = \frac{3}{4}

    2x = arcsin {\frac{3}{4}}

    x = \frac{1}{2} arcsin {\frac{3}{4}}
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  3. #3
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    please can you explain where did 2cos40cosx and +4sin40sinx come from?
    Last edited by snowball; September 16th 2008 at 12:29 AM. Reason: I just understood where it came from, thanks again!
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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by snowball View Post


    please can you explain where did 2cos40cosx and +4sin40sinx come from?
    He added like terms

    cos 40 cos x - sin 40 sin x = 3 cos 40 cos x + 3 sin 40 sin x

     -4 sin 40 sin x = 2 cos 40 cos x

     0 = 2 cos 40 cos x +4 sin 40 sin x
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