Question

Graphically find `x` for which `sinx=cosx`?

Answer 1

Please see below.

Explanation:

As `sin(x+pi/2)=cosx`, `sinx` function moves with a gap of `pi/2` with respect to `cosx`. Between `x=0` and `x=pi/2`, `cosx` falls from `1` to `0`and `sinx` rises from `0` to `1`.

Further `cos(-x)=cosx` and hence while `cosx` is symmetric around `y`-axis i.e. `x=0`, As `sinx` appears with a lag of `pi/2`, it is symmetric around `x=pi/2`.

Hence, `cosx=sinx` appears exactly at the midpoint between `0` and `pi/2` i.e. at `pi/4=0.7854`
graph{(y-sinx)(y-cosx)=0 [-1.365, 3.635, -1, 1.5]}