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Math Help - What's the difference between these two trig identity problems?

  1. #1
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    What's the difference between these two trig identity problems?

    1) 2 \tan x=3 \sin x
    2 \frac{\sin x}{\cos x}=3 \sin x \rightarrow 2 \sin x = 3 \sin x \cos x \rightarrow \sin x(2 - 3 \cos x)=0
    a) \sin x = 0 \rightarrow x =180n
    b) \cos x = \frac{2}{3} \rightarrow x =48.19 + 360n

    2) 2 \sin 2x \cos ^2 x = \sin 2x
    \sin 2x(2 \cos ^2 x -1) =0 \rightarrow
    a) \sin 2x=0 \rightarrow 2x=180n \rightarrow x = 90n
    b) \cos ^2 x = \frac{1}{2} \rightarrow \cos x = \pm \sqrt{\frac{1}{2} }
    x = \pm 45 + 360n

    of course the answer to number 2 is \pm 45 + 180n
    but the answer to number 1 is 48.19 + 360n! So what's the difference between the two? They are both cosine functions. I just thought always add 360 degrees because that's when the angle repeats itself.

    (*fixed the bold...)
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  2. #2
    Pim
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    \cos x = \pm \frac{1}{2}\sqrt{2} has four solutions on [0,360]
    These are 45, 135, 225 and 315
    45 + 360n and 135 + 360n can be rewritten as 45+180n, because they are half a period apart.
    Same goes for 135 and 315 (where -45 is 315-360)
    You could sum up all solutions as 45+90n

    Do you understand now?
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  3. #3
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    touche
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