# Find all values of x in the interval [0, 2pi] that satisfy the equation: 3cot^2 x=1

Ellen Chang 2022-07-16 Answered
Find all values of x in the interval $\left[0,2\pi \right]$ that satisfy the equation:
$3{\mathrm{cot}}^{2}x=1$
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karburitc
$3{\mathrm{cot}}^{2}x=1$
${\mathrm{cot}}^{2}x=\frac{1}{3}$
$\mathrm{cot}x=±\sqrt{\frac{1}{3}}$
$\mathrm{cot}x=±\frac{1}{\sqrt{3}}$
$\frac{\mathrm{cos}x}{\mathrm{sin}x}=±\frac{1}{\sqrt{3}}$
$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}\ast \frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}$
$x=\frac{\pi }{3};\frac{3\pi }{3}$
$\frac{2\pi }{3};\frac{4\pi }{3}$
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Jeffrey Jordon

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