Find all values of x in the interval $[0,2\pi ]$ that satisfy the equation:

$3{\mathrm{cot}}^{2}x=1$

$3{\mathrm{cot}}^{2}x=1$

Ellen Chang
2022-07-16
Answered

Find all values of x in the interval $[0,2\pi ]$ that satisfy the equation:

$3{\mathrm{cot}}^{2}x=1$

$3{\mathrm{cot}}^{2}x=1$

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karburitc

Answered 2022-07-17
Author has **7** answers

$3{\mathrm{cot}}^{2}x=1$

${\mathrm{cot}}^{2}x=\frac{1}{3}$

$\mathrm{cot}x=\pm \sqrt{\frac{1}{3}}$

$\mathrm{cot}x=\pm \frac{1}{\sqrt{3}}$

$\frac{\mathrm{cos}x}{\mathrm{sin}x}=\pm \frac{1}{\sqrt{3}}$

$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}\ast \frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}$

$x=\frac{\pi}{3};\frac{3\pi}{3}$

$\frac{2\pi}{3};\frac{4\pi}{3}$

${\mathrm{cot}}^{2}x=\frac{1}{3}$

$\mathrm{cot}x=\pm \sqrt{\frac{1}{3}}$

$\mathrm{cot}x=\pm \frac{1}{\sqrt{3}}$

$\frac{\mathrm{cos}x}{\mathrm{sin}x}=\pm \frac{1}{\sqrt{3}}$

$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}\ast \frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}$

$x=\frac{\pi}{3};\frac{3\pi}{3}$

$\frac{2\pi}{3};\frac{4\pi}{3}$

Jeffrey Jordon

Answered 2022-08-01
Author has **2313** answers

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