Question

Which of the following is the graph of $sin|x|$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$sin|x|$

Let's try to find out $sin|x|$ for some negatvie values of x.

$sin|x|atx=\frac{-\pi }{2}=sin\left|\frac{-\pi }{2}\right|=sin\frac{\pi }{2}=1$

$sin|x|atx=-\frac{\pi }{6}=sin\left|\frac{-\pi }{6}\right|=sin\frac{\pi }{6}=\frac{1}{2}$

What we observe is that the value of $sin|x|atx=-\frac{\pi }{2}and\frac{-\pi }{6}$ are same as $sin\frac{\pi }{2}$ and $sin\frac{\pi }{6}$. While drawing

the graph of $sin|x|$, we will draw it for positive values of x and then extend it for negative values. We

can also say we will remove the part on negative x-axis and take the reflection of the part on +ve x-axis.

So, the graph will look like in option D