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Math Help - Solutions for sin and cos equations

  1. #1
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    Solutions for sin and cos equations

    Really need help with how to figure these out.

    Solutions for sin and cos equations-math.png

    Thanks
    James
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solutions for sin and cos equations

    For the first one, rewrite the equation using the double-angle identity for sine, to get:

    2\sin(x)\cos(x)=\sqrt{2}\cos(x)

    Now, divide through by \sqrt{2} then subtract \cos(x) from both sides, factor and use the zero-factor property to equate both factors to zero and solve.

    For the second one, use a Pythagorean identity to get a quadratic in \sin(x) :

    2(1-\sin^2(x))+3\sin(x)=3

    Now, distribute, and arrange in standard quadratic form, and you will find it factors nicely, and use the zero-factor property to equate both factors to zero and solve.
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  3. #3
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    Re: Solutions for sin and cos equations

    James this is very easy

    for the first remember that sin(2x) =2sinxcosx
    therefore 2sinxcosx=sqrt(2)cosx
    transfer to the frst term and factorize to find
    cosx =0 and sinx=sqrt(2)/2 solve them .....

    for the second substitute cos^2(x) =1-sin^2(x) and solve the quadratic equation that you will obtain for sinx ..it is easy
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  4. #4
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    Re: Solutions for sin and cos equations

    omg, thank you so much Mark and Mino!!!
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