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Math Help - trig general solution

  1. #1
    Member srirahulan's Avatar
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    Exclamation trig general solution

    cosx-sin3x=\sqrt2
    6cos^2x+8sinxcosx=0

    How can I solve this equation and find out the general solution.Please give me any idea.
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  2. #2
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    Re: trig general solution

    Quote Originally Posted by srirahulan View Post
    cosx-sin3x=\sqrt2
    6cos^2x+8sinxcosx=0

    How can I solve this equation and find out the general solution.Please give me any idea.
    The second factorises very easily. Set each factor equal to 0.
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  3. #3
    Member srirahulan's Avatar
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    Re: trig general solution

    Ok Thanks,how can I solve first one?
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  4. #4
    Member kalyanram's Avatar
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    Re: trig general solution

    Write cosx=sin(\frac{\pi}{2}-x) and use trigonometric transformation the equation becomes cos(\frac{\pi}{4}+x)sin(\frac{\pi}{4}-2x)=\frac{1}{\sqrt{2}}
    Look for sign changes of this function in the interval [0,2\pi] the roots are as shown in this link cos(pi/4+x)sin(pi/4 -2x) - 1/sqrt(2) - Wolfram|Alpha
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  5. #5
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    Re: trig general solution

    This is one of the best techniques to solving problems (not just mathematical by the way, but problems in general) and this is the first thing you should do any of these sorts of geometry problems. nike free running nike free running shoes for women nike free 3.0
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  6. #6
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    Re: trig general solution

    Or, you will get a cubic in Sin^2(x) or cos^2(x), solve it using Cubic function - Wikipedia, the free encyclopedia.

    Salahuddin
    Maths online
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