$\mathrm{sin}x=\mathrm{tan}x$

veneciasp
2022-07-13
Answered

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

$\mathrm{sin}x=\mathrm{tan}x$

$\mathrm{sin}x=\mathrm{tan}x$

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Jayvion Mclaughlin

Answered 2022-07-14
Author has **14** answers

$\mathrm{sin}x=\mathrm{tan}x$

$\mathrm{sin}x=\frac{\mathrm{sin}x}{\mathrm{cos}x}$

$\mathrm{sin}x-\frac{\mathrm{sin}x}{\mathrm{cos}x}=0$

$\mathrm{sin}x(1-\frac{1}{\mathrm{cos}x})=0$

$1-\frac{1}{\mathrm{cos}x}=0$

$1=\frac{1}{\mathrm{cos}x}$

$\mathrm{cos}x=1$

$\mathrm{sin}x=0;$

$x=0;\pi ;2\pi $

$\mathrm{sin}x=\frac{\mathrm{sin}x}{\mathrm{cos}x}$

$\mathrm{sin}x-\frac{\mathrm{sin}x}{\mathrm{cos}x}=0$

$\mathrm{sin}x(1-\frac{1}{\mathrm{cos}x})=0$

$1-\frac{1}{\mathrm{cos}x}=0$

$1=\frac{1}{\mathrm{cos}x}$

$\mathrm{cos}x=1$

$\mathrm{sin}x=0;$

$x=0;\pi ;2\pi $

Jeffrey Jordon

Answered 2022-08-01
Author has **2495** answers

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Eventually I get

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The answer I obtained is the only answer, another respective value of x in 4-th quadrant does not solve the equation, how does this happen? I have been facing the same problem every time I solved this kind of trigonometric equation.

Find x for $0<x<2\pi $

Eventually I get

$\mathrm{cos}x=\frac{8}{17}$

$x={61.9}^{\circ}$

The answer I obtained is the only answer, another respective value of x in 4-th quadrant does not solve the equation, how does this happen? I have been facing the same problem every time I solved this kind of trigonometric equation.

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