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Math Help - Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

  1. #1
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    Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Stuck on this question, Thanks for your help.
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  2. #2
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Quote Originally Posted by UrgedTaylor View Post
    Stuck on this question, Thanks for your help.
    When you have an equation equal to zero,
    like this one,
    the simplest strategy is to find a common term and write factors.
    Then use the fact that zero multiplied by anything is zero.
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  3. #3
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    You can factor out \cos(x) to give \cos(x)(\sqrt{3}\tan(x) + 1) = 0

    Hence either \cos(x) = 0 \text{  or  } \sqrt{3}\tan(x)+1=0
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Thanks both of you, but i am still having issues. I'm doing a practice provincial exam for Pmath 12 and I haven't done this stuff in half a year ( also the unit I struggled the most with).

    Here are the possible answer's:
    A- (pi)/6 and 7(pi)/6
    B-5(pi)/6 and 11(pi/6
    C- (pi)/6 and 7(pi)/6 and (pi)/2 and 3(pi)/2
    D-5(pi)/6 and 11(pi/6 and (pi)/2 and 3(pi)/2


    Thanks for any further help
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Which of the answers look correct to you,
    based on post 3 ?
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    I'm sure it will be either C or D, but that's about all I can tell so far because I know cos(pi)/2 and cos 3(pi)/2 =0 and I know there will be 2 more answers
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Quote Originally Posted by UrgedTaylor View Post
    I'm sure it will be either C or D, but that's about all I can tell so far because I know cos(pi)/2 and cos 3(pi)/2 =0 and I know there will be 2 more answers
    Yes, the other answers come from the 2nd factor.
    You need to rearrange that for tanx, so that you can find the angles
    associated with tanx.
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Figured out it is D Because √3tanx is negative 1 in quadrants 3 and 4. Thank you again
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    \begin{aligned}   \sqrt{3}\cos{x}\tan{x}+\cos{x} & = \sqrt{3}\sin{x}+\cos{x} \\&= 2\bigg(\frac{\sqrt{3}}{2}\sin{x}+\frac{1}{2}\cos{x  }\bigg) \\& = 2\bigg(\cos{\frac{\pi}{6}}~\sin{x}+\sin{\frac{\pi}  {6}}\cos{x}\bigg) \\& = 2\sin\left(x+\frac{\pi}{6}\right).\end{aligned}
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Well, it's actually negative in quadrants 2 and 4,
    because tanx gives the slope of a line through the origin.
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Do you know which values of \displaystyle x make \displaystyle \tan{x} = \frac{1}{\sqrt{3}}?
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    Re: Solve √3 cosxtanx+ cosx=0 , where 0≤x<2(Pi)

    Quote Originally Posted by Prove It View Post
    Do you know which values of \displaystyle x make \displaystyle \tan{x} = \frac{1}{\sqrt{3}}?
    \pi/6 \bmod \pi ?
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