Question

Match the following graphs with respective trigonometric ratio:

• A. $\sin x$
• B. $\cos x$
• C. $\tan x$

Answer 1

If we plot the values of known angles for $\sin x,\cos x,$ and $\tan x$ and join them to get the respective graphs.

Let us try to plot $\sin x$

at $x=0,\sin x=0$

at $x=\frac{\pi }{2},\sin x=1$

at $x=\pi ,\sin x=0$

at $x=\frac{3\pi }{2},\sin x=-1$

at $x=2\pi ,\sin x=0$

$\sin x$ is periodic with a period of $2\pi$
$\Rightarrow \sin (2\pi +x)=\sin x$
So, we will plot for the interval $[0,2\pi ]$ and replicate.

We can do the same for remaining functions.

Graph of $\cos x$:

$\tan x$ is 0 at $x=0$ and infinity at $x=\frac{\pi }{2}$

Graph for $\tan x$: