Question

sketch the graph of y =sine3x​

Answer 1

The graph of $\mathbf{y=\sin{3x}}$ is given by,

Here given the function is $y=\sin{3x}$

when $x=0\Rightarrow y=\sin{3\times 0}=\sin0=0$, then it passes through the origin (0,0).

When $x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1$

Since we know that, $-1\leq\sin{x}\leq1,\forall x$, then the function has maximum height at $x=\frac{\pi}{6}$.

Again when $x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0$, again the function is 0.

So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.

Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2

Using graphing calculator we get the graph of function $y=\sin3x$,

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