Trig Equations Question Prelim 3unit (1 Viewer)

OH1995 · Mar 20, 2012

Stumped on this question, help would be appreciated. Thanks!

2sin²x+cosx=2

nightweaver066 · Mar 20, 2012

OH1995 said:
Stumped on this question, help would be appreciated. Thanks!

2sin²x+cosx=2

You mean solve for x?

$2sin^2x + cosx = 2$

$$Recall Pythagorean identity: $ sin^2x + cos^2x = 1$

$sin^2x = 1 - cos^2x$

$Using this,$

$2(1 - cos^2x) + cosx = 2$

$2 - 2cos^2x + cosx = 2$

$2cos^2x - cosx = 0$

$cos(2cosx - 1) = 0$

$I'm going to assume the domain of solutions is restricted between 0 and 360$

$cosx = 0, 2cosx - 1 = 0$

$cosx = 0, cosx = \frac{1}{2}$

$x = 60, 90, 270, 330$

deswa1 · Mar 20, 2012

$2sin^2x+cosx-2=0\\ 2(1-cos^2x)+cosx-2=0\\ -2cos^2x+cosx=0\\ -cosx(2cosx-1)=0\\ cosx=0\textup{ OR }cosx=\frac{1}{2}\\ x=\frac{\pi}{2} \textup{ OR }x=\frac{\pi}{3}$

I thought for sure I'd be the first poster... (That was like my fastest latex ever)

nightweaver066 · Mar 20, 2012

deswa1 said:
$2sin^2x+cosx-2=0\\ 2(1-cos^2x)+cosx-2=0\\ -2cos^2x+cosx=0\\ -cosx(2cosx-1)=0\\ cosx=0\textup{ OR }cosx=\frac{1}{2}\\ x=\frac{\pi}{2} \textup{ OR }x=\frac{\pi}{3}$

I thought for sure I'd be the first poster... (That was like my fastest latex ever)

Haha this is my fastest latex yet as well.

deswa1 · Mar 20, 2012

Ah well, congrats

. Maybe next time I'll be first...

Trig Equations Question Prelim 3unit (1 Viewer)

OH1995

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nightweaver066

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