Question

Giải phương trình: \(sin\left(x+\dfrac{\pi}{4}\right)=-\dfrac{\sqrt{3}}{2}\)

Answer 1

`sin(x+\pi/4)=-\sqrt{3}/2`

`<=>[(x+\pi/4=-\pi/3+k2\pi),(x+\pi/4=[4\pi]/3+k2\pi):}`

`<=>[(x=[-7\pi]/12+k2\pi),(x=[13\pi]/12+k2\pi):}`    `(k in ZZ)`

Answer 2

  

Answer 3

=>  sin ( x + \(\dfrac{\pi}{4}\) ) = sin ( \(-\dfrac{\pi}{3}\) )

TH1 : x +\(\dfrac{\pi}{4}\) = \(-\dfrac{\pi}{3}\) + k2\(\pi\)

(=) x = \(\dfrac{-7\pi}{12}\) +  k2\(\pi\)

TH2 : x +\(\dfrac{\pi}{4}\) = \(\pi+\) \(\dfrac{\pi}{3}\) + k2\(\pi\)

(=) x = \(\dfrac{13\pi}{12}\) + k2\(\pi\)