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

1 Answer
Jul 11, 2017

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