need help with these questions -

solve sin(2x-45) = √ 3 / 2

and

find general solutions of sin2x=cosx

thankyou in advance :)

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- Apr 27th 2012, 02:47 AMjshine96trig question
need help with these questions -

solve sin(2x-45) = √ 3 / 2

and

find general solutions of sin2x=cosx

thankyou in advance :) - Apr 27th 2012, 02:55 AMProve ItRe: trig question
$\displaystyle \displaystyle \begin{align*} \sin{(2x - 45)} &= \frac{\sqrt{3}}{2} \\ 2x - 45 &= \left\{ 60, 120 \right\} + 360n , n \in \mathbf{Z} \end{align*}$

Go from here.

$\displaystyle \displaystyle \begin{align*} \sin{2x} &= \cos{x} \\ 2\sin{x}\cos{x} &= \cos{x} \\ 2\sin{x}\cos{x} - \cos{x} &= 0 \\ \cos{x}\left(2\sin{x} - 1\right) &= 0 \\ \cos{x} = 0 \textrm{ or } 2\sin{x} - 1 &= 0 \end{align*}$

Go from here. - Apr 27th 2012, 03:00 AMskeeterRe: trig question
- Apr 27th 2012, 03:09 AMjshine96Re: trig question
sorry, i forgot to add -

solve sin(2x-45) = √ 3 / 2 for -180 ≤ x ≤ 180 - Apr 27th 2012, 03:12 AMProve ItRe: trig question
- Apr 27th 2012, 03:25 AMjshine96Re: trig question
sorry.. i still don't get how to solve it :L [i get the first part]

- Apr 27th 2012, 03:33 AMjshine96Re: trig question
and for this question find general solutions of sin2x=cosx

i understand what you wrote, but confused on what to do next.. do I solve what x is? like 90, 27, 30, 150?