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Math Help - More trig equations.

  1. #1
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    More trig equations.

    The first one is
    sinx+cosx=0 solve between 0 and 2pi
    See I am not sure how to start this one?

    The next question is find find for all real values of x

    3tanx^2= square root 3 tanx Also the square root only covers 3
    So to do this one would I have to square the square root of 3 on one side
    Then on the other side do (3tanx^2)(3tan^2x)
    Also the x is on the tan not on the exponent.
    Last edited by mr fantastic; March 6th 2011 at 01:16 AM. Reason: Moved from another thread.
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    The first one is
    sinx+cosx=0 solve between 0 and 2pi <--- (A)
    See I am not sure how to start this one?

    The next question is find find for all real values of x

    3tanx^2= square root 3 tanx <--- (B)
    Also the square root only covers 3
    So to do this one would I have to square the square root of 3 on one side
    Then on the other side do (3tanx^2)(3tan^2x)
    Also the x is on the tan not on the exponent.
    to (A):

    \sin(x)+\cos(x)=0~\implies~ \sin(x)=-\cos(x) Divide by cos(x)

    \tan(x)=-1

    Use your calculator and the \tan^{-1}-mode.

    To (B):

    3\tan^2(x)=\sqrt{3} \cdot \tan(x)~\implies~3\tan^2(x) - \sqrt{3} \cdot \tan(x) = 0 Factor out 3tan(x):

    3\tan(x)\left(\tan(x)-\dfrac1{\sqrt{3}}\right)=0

    A product equals zero if one factor equals zero. Therefore you have to solve for x:

    3\tan(x)=0~\vee~\tan(x)-\frac1{\sqrt{3}}=0

    Use your calculator and the \tan^{-1}-mode.
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