Solution 4.4:7a
From Förberedande kurs i matematik 1
If we examine the equation, we see that
If we write
and it is expressed completely in terms of
 t+41 2−412−21=t+412−916 |
and then obtain the equation
| t+412=916 |
which has the solutions 
916=−4143
Because
This equation has the solutions \displaystyle x = \pi/6 and \displaystyle x = \pi - \pi/6 = 5\pi/6 in the unit circle and the general solution is
| \displaystyle x = \frac{\pi}{6}+2n\pi\qquad\text{and}\qquad x = \frac{5\pi}{6}+2n\pi\,, |
where n is an arbitrary integer.
\displaystyle \sin x = -1:
The equation has only one solution \displaystyle x = 3\pi/2 in the unit circle, and the general solution is therefore
| \displaystyle x = \frac{3\pi}{2} + 2n\pi\,, |
where n is an arbitrary integer.
All of the solution to the equation are given by
| \displaystyle \left\{\begin{align}
x &= \pi/6+2n\pi\,,\\[5pt] x &= 5\pi/6+2n\pi\,,\\[5pt] x &= 3\pi/2+2n\pi\,, \end{align}\right. |
where n is an arbitrary integer.
