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

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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. 

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