What do roots in trigonometry mean? Why does solving some trigonometric equations give you multiple solutions?

In solving trig, or other equations, finding the "roots" means to find the solutions.  This also means find the values when "theta" or "x" is zero.  Also known as the x-intercepts.

Trig equations often have multiple solutions because there are multiple angle measurements which give you the same value on a trig graph.  

For instance, consider the trig equation `sinx = sqrt(2)/2`

Since sin45 = `sqrt(2)/2` and sin135 =`sqrt(2)/2` so both x = 45 and x = 135 are solutions to the trig equation

There are even more solutions to this equation since trig functions are periodic--meaning that answers repeat themselves every 360 degrees. So x = 45 + 360 = 405 is also a solution.