How do you solve $cos θ tan θ + \sqrt{3} cos θ = 0$ $Cos theta Tan theta+sqrt(3)Cos theta=0$ for [0,2pi]?

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How do you solve $cos θ tan θ + \sqrt{3} cos θ = 0$ $Cos theta Tan theta+sqrt(3)Cos theta=0$ for [0,2pi]?

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Answer 1 · 2015-09-26T12:19:49

$θ = \frac{5 π}{6}$ $theta = (5pi)/6$ and $\frac{11 π}{6}$ $(11pi)/6$

Explanation:

$cos θ \cdot (\frac{sin θ}{cos θ}) + \sqrt{3} cos θ = 0$ $costheta * (sintheta /costheta) + sqrt3costheta =0$

You know that $tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta /costheta$ , which means that you have

$sin θ + \sqrt{3} cos θ = 0$ $sintheta + sqrt3costheta =0$

$sin θ = - \sqrt{3} \cdot cos θ$ $sintheta = - sqrt3 * costheta$

$tan θ = - \sqrt{3}$ $tantheta =-sqrt3$ for $[0, 2 π]$ $[0,2pi]$ ,

$θ = π - (\frac{π}{3})$ $theta = pi - (pi/3)$ and $2 π - (\frac{π}{3})$ $2pi - (pi/3)$

$θ = \frac{5 π}{6}$ $theta = (5pi)/6$ and $\frac{11 π}{6}$ $(11pi)/6$

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How do you solve $cos θ tan θ + \sqrt{3} cos θ = 0$ $Cos theta Tan theta+sqrt(3)Cos theta=0$ for [0,2pi]?

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How do you solve Cos theta Tan theta+sqrt(3)Cos theta=0cosθtanθ+√3cosθ=0Cos theta Tan theta+sqrt(3)Cos theta=0 for [0,2pi]?

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How do you solve $cos θ tan θ + \sqrt{3} cos θ = 0$ $Cos theta Tan theta+sqrt(3)Cos theta=0$ for [0,2pi]?