solving trig equations (1 Viewer)

maths lover · Mar 28, 2011

solve sin cubed x +2sin squaredx cosx +sinx cos squared x =0 between 0 and 360 dgrees

ohexploitable · Mar 28, 2011

maths lover said:
solve sin cubed x +2sin squaredx cosx +sinx cos squared x =0 between 0 and 360 dgrees

$\\\sin^3x+2\sin^2x\cos x+\sin x\cos^2x=0\\\sin x(\sin^2x+2\sin x\cos x+\cos^2x)=0\\\sin x(\sin x+\cos x)^2=0$

$\\\sin x=0,\, \sin x+\cos x=0\\\sin x=0,\,\tan x+1=0\text{ (divide everything by }\cos x)$

I'm sure you can solve it from there

SpiralFlex · Mar 28, 2011

$\sin ^3x + 2\sin x \cos x + \sin x \cos^2x = 0$

$\sin x (\sin^2 x + 2\sin x \cos x + \cos^2x) = 0$

$\sin x(\sin x + \cos x)^2 = 0$

$\therefore \sin x = 0$ and $\therefore \sin x + \cos x = 0$

Dividing all sides for the second one by $\cos x$ and moving it to get,

$\tan x = -1$

Now,

For $\sin x = 0$ , read off the sine graph or if you are lazy enter it on the calculator.

For $\tan x = -1$ , it is in the 2nd and 4th quadrant.

$\therefore x = 0, 135, 180, 315, 360$ degrees of course and if you love your radians $x = 0, \frac{3\pi}{4}, \pi, \frac{7\pi}{4}, 2\pi$ .

HyperComplexxx · Mar 28, 2011

hump hump

maths lover · Mar 29, 2011

thanks guys really appreciated

blackops23 · Mar 30, 2011

sin x + cos x = 0 --> 1+ tanx = 0, the simplicity is just too brilliant...!

solving trig equations (1 Viewer)

maths lover

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ohexploitable

hey

SpiralFlex

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HyperComplexxx

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maths lover

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blackops23

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