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

1 Answer
Shwetank Mauria
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#

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