What are the different ways one can predict the sign of Trigonometric functions. The function may contain combination of different functions.
let us suppose I have a function f(x)= sin(2x) - cos(3x)
Now I want to predict the sign of this function in the interval [0,2π].
Is there any mechanical(doing some math calculations) approach or it is a matter of fact that you have to remember the graphs of both the functions and have a good idea of what will be the result (without actually calculating any thing).
However I can predict the nature of the function f(x) using this graph [pink-->Resultant || green-->cos(3x) || violet-->sin(2x)] ]1
please admit if you have some shortcut or any trick to quickly predict the sign. sorry for my bad English :(