Cos(2x)=-(√2)/2

Can anyone help me solve this?

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- Nov 2nd 2008, 10:12 PMssmhTrig identities
Cos(2x)=-(√2)/2

Can anyone help me solve this? - Nov 2nd 2008, 11:07 PM11rdc11
I kind of sleepy so hopefully I don't make a mistake lol

$\displaystyle \cos{(2x)}=-\frac{\sqrt{2}}{2}$

Ok so you know cos is negative in the 2nd and 3rd quadrant.

Also $\displaystyle \cos{x} = -\frac{\sqrt{2}}{2}$ at 135 degrees and 225

Now just divide 135 and 225 by 2 and it will give you your answer

$\displaystyle 67.5 + 360n$

$\displaystyle 112.5 + 360n$

$\displaystyle n = 0,\pm 1, \pm 2,...$