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

$2\mathrm{cos}x=-\mathrm{sin}2x$

$2\mathrm{cos}x=-\mathrm{sin}2x$

pipantasi4
2022-07-15
Answered

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

$2\mathrm{cos}x=-\mathrm{sin}2x$

$2\mathrm{cos}x=-\mathrm{sin}2x$

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Asdrubali2r

Answered 2022-07-16
Author has **14** answers

$2\mathrm{cos}x=-\mathrm{sin}2x$

$2\mathrm{cos}x=-2\mathrm{sin}x\mathrm{cos}x$

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

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

$\mathrm{cos}x=0\text{}\text{}\text{}\mathrm{sin}x=-1$

$x=\frac{\pi}{2};\frac{3\pi}{2}\text{}\text{}\text{}x=\frac{3\pi}{2}$

$2\mathrm{cos}x=-2\mathrm{sin}x\mathrm{cos}x$

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

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

$\mathrm{cos}x=0\text{}\text{}\text{}\mathrm{sin}x=-1$

$x=\frac{\pi}{2};\frac{3\pi}{2}\text{}\text{}\text{}x=\frac{3\pi}{2}$

Jeffrey Jordon

Answered 2022-08-01
Author has **2581** answers

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Finding the general solution of a trigonometric equation

Find the general solution of the equation

$$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-8{\mathrm{cos}}^{2}x=-2$$

My working:

$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-8{\mathrm{cos}}^{2}x+2=0$

$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x+8{\mathrm{sin}}^{2}x-6=0$

$\text{}10{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-6=0$

$\text{}5-5\mathrm{cos}2x+5\mathrm{sin}x\mathrm{cos}x-6=0$

I am giving my working for the sake of it...I know I'm getting nowhere. I really need a hint as to how I can take this forward.

Find the general solution of the equation

$$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-8{\mathrm{cos}}^{2}x=-2$$

My working:

$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-8{\mathrm{cos}}^{2}x+2=0$

$\text{}2{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x+8{\mathrm{sin}}^{2}x-6=0$

$\text{}10{\mathrm{sin}}^{2}x+5\mathrm{sin}x\mathrm{cos}x-6=0$

$\text{}5-5\mathrm{cos}2x+5\mathrm{sin}x\mathrm{cos}x-6=0$

I am giving my working for the sake of it...I know I'm getting nowhere. I really need a hint as to how I can take this forward.