Question

Which of the following is the sketch of the graph $y=\left(\frac{|cosx|}{cosx}\right)$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$y=\frac{|cosx|}{cosx}$

Here, $y=\{\begin{array}{cc}1;& cosx>0\\ -1;& cosx<0\end{array}$

Graph of $y=cosx$

we can observe from the graph

cosx is positive when

$2n\pi -\frac{\pi }{2}$< x<$2n\pi +\frac{\pi }{2}$

cosx is nagative when

$2n\pi +\frac{\pi }{2}$< x<$2n\pi +\frac{3\pi }{2}$

$y=\{\begin{array}{cc}1& 2n\pi -\frac{\pi }{2}<x<2n\pi +\frac{\pi }{2}\\ -1& 2n\pi +\frac{\pi }{2}<x<2n\pi +\frac{3\pi }{2}\end{array}$

when $cosx=0,y=\frac{|cosx|}{cosx}$ is not defined.

so,it should be plotted as: