Question

Which quadrants and axes does `f(x)=cos^2x` pass through?

Answer 1

`f(x)=cos^2x` is always `0` or positive and can take any value between `[0,1]` and it touches `x` at `x=(2k+1)pi/2` and passes only through `Q1` and `Q2`

Explanation:

`cosx` can take values only between `[-1,1]`, further when `x=2kpi` `cosx=1` and when `x=(2k+1)pi` `cosx=-1` and at `x=(2k+1)pi/2`, `cosx=0`

`f(x)=cos^2x` is always `0` or positive and can take any value between `[0,1]` and it touches `x`-axis at `x=(2k+1)pi/2`

Hence it passes only through `Q1` and `Q2`

and while it touches `x`-axis at `x=(2k+1)pi/2`, it crosses `y` axis at `x=0`