Consider the equation \sin 2 x = \sqrt{\dfrac{3}{2}} - \cos 2 x.
Find all of the solutions to the equation in the interval 0 \leq x < 2 \pi.
Given that n represents an integer, find an expression for the general solutions to the equation \sin 2 x = \sqrt{\dfrac{3}{2}} - \cos 2 x.
Find the general solution of the following equations, using n to represent an integer:
\sin x = \dfrac{1}{2}
\cos x = - \dfrac{\sqrt{3}}{2}
\sin x = \dfrac{\sqrt{3}}{2}
\tan x =-\sqrt{3}
Find the general solution of the following equations, using n to represent an integer:
2 \sin x = -\sqrt{3}
\sqrt{3} \tan \left(\dfrac{x}{2}\right) = - 3
\sin 2 x = \dfrac{1}{\sqrt{2}}
2 \sin 3 x - \sqrt{2} = 0
\sin x = - \cos x
\cos \left(\dfrac{x}{2}\right) = 1 - \cos \left(\dfrac{x}{2}\right)
Find the general solution of the following equations, using n to represent an integer:
2 \sin ^{2} x = 1
\tan ^{2}3x = \dfrac{1}{3}
\cos ^{2}\left(\dfrac{x}{2}\right) - 1 = 0
\sin ^{2}\left(\dfrac{x}{2}\right) - \dfrac{3}{4} = 0
Find the general solution of the following equations, using n to represent an integer:
\cos \left(x + \dfrac{\pi}{4}\right) = - \dfrac{1}{\sqrt{2}}
Find the general solution of the following equations, using n to represent an integer:
\cos ^{2} x + \cos x = 0
\cos x \tan x = \cos x