The basic trigonometric functions – sin, cos, tan – have many symmetries. All are
periodic, repeating everyor 360 degrees. In addition:
cos is symmetric about
so
In fact cos is symmetric about
for any integer
so
sin is symmetric about
and
so that
and 
In fact sin is symmetric about
so
for any integer
tan isperiodic so
In fact
for any integer
These symmetries are illustrated below.
These symmetries allow us to write down general solutions of simple trigonometric equations.
Example: Find the general solution of the equation
The general solution is then
Example: Find the general solution of the equation
The general solution is then
Example: Find the general solution of the equation
The general solution is then