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Math Help - simple trig equation

  1. #1
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    Exclamation simple trig equation

    sin (x + PI/3) = cos (x PI/3). Solve for x.

    Hi

    Could someone please help me solve the above question? For some reason I can't seem to get x.

    I end up with:

    sin x + root(3) cos x = cos x + root(3) sin x
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  2. #2
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    Hello,
    Quote Originally Posted by xwrathbringerx View Post
    sin (x + PI/3) = cos (x PI/3). Solve for x.

    Hi

    Could someone please help me solve the above question? For some reason I can't seem to get x.

    I end up with:

    sin x + root(3) cos x = cos x + root(3) sin x
    A way to solve is to note that \sin(t)=\cos(\pi/2 -t)

    Then \sin(x+\pi/3) can be transformed into \cos\left(\tfrac\pi 2-\tfrac\pi 3-x\right)=\cos(\pi/6-x)

    Then, two possibilities :
    - use the trigonometric identity \cos(a)-\cos(b)=-2\sin\left(\tfrac{a+b}{2}\right)\sin\left(\tfrac{a-b}{2}\right)

    - or recall that \cos(a)=\cos(b)\Leftrightarrow a=\pm b+2k\pi\text{ where k is an integer} (you can easily see that on a unit circle)
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