Which quadrants and axes does f(x)=cos^2xf(x)=cos2x pass through?

1 Answer
Jul 11, 2017

f(x)=cos^2xf(x)=cos2x is always 00 or positive and can take any value between [0,1][0,1] and it touches xx at x=(2k+1)pi/2x=(2k+1)π2 and passes only through Q1Q1 and Q2Q2

Explanation:

cosxcosx can take values only between [-1,1][1,1], further when x=2kpix=2kπ cosx=1cosx=1 and when x=(2k+1)pix=(2k+1)π cosx=-1cosx=1 and at x=(2k+1)pi/2x=(2k+1)π2, cosx=0cosx=0

f(x)=cos^2xf(x)=cos2x is always 00 or positive and can take any value between [0,1][0,1] and it touches xx-axis at x=(2k+1)pi/2x=(2k+1)π2

Hence it passes only through Q1Q1 and Q2Q2

and while it touches xx-axis at x=(2k+1)pi/2x=(2k+1)π2, it crosses yy axis at x=0x=0