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Math Help - please help me

  1. #1
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    please help me

    Find the line passing through the given point and making the given angle with the given line. (2, 1), π/4, 2x 3y + 2 = 0
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  2. #2
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    Re: please help me

    Quote Originally Posted by mackyme View Post
    Find the line passing through the given point and making the given angle with the given line. (2, 1), π/4, 2x 3y + 2 = 0
    The first line can be written as \displaystyle \begin{align*} y = \frac{2}{3}x + \frac{2}{3} \end{align*}, which has a gradient of \displaystyle \begin{align*} \frac{2}{3} \end{align*}.

    You should know that the gradient \displaystyle \begin{align*} m_1 \end{align*} makes the line make an angle \displaystyle \begin{align*} \theta_1 \end{align*}with the positive x axis, such that \displaystyle \begin{align*} \tan{\theta_1} = m \end{align*}. So from this line we can see

    \displaystyle \begin{align*} \tan{\theta_1} &= \frac{2}{3} \\ \theta_1 &= \tan^{-1}\left(\frac{2}{3}\right) \\ \theta_1 &\approx 0.588 \end{align*}


    You should also know that if you have two lines and know the angles they make with the positive x axis, then the angle between them \displaystyle \begin{align*} \theta \end{align*} can be evaluated by \displaystyle \begin{align*} \theta = \theta_2 - \theta_1 \end{align*}.

    You have \displaystyle \begin{align*} \theta \end{align*}, you have \displaystyle \begin{align*} \theta_1 \end{align*}. Can you evaluate \displaystyle \begin{align*} \theta_2 \end{align*} and use this to find the gradient of the line you are trying to find the equation of? From there can you find the equation of the line?
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