Sketch the Graph of f(x) = 2 sin x for 0 ≤ x ≤ π
Question:
Sketch the graph of the following function :
\[ f(x)=2\sin x,\quad 0 \le x \le \pi \]
Solution:
We know that the graph of \(y=\sin x\) is a sine curve.
Since the function is
\[ y=2\sin x \]
therefore the sine curve is stretched vertically by factor \(2\).
Now find some important points:
\[ \begin{aligned} x=0 &\Rightarrow y=2\sin0=0\\ x=\frac{\pi}{2} &\Rightarrow y=2\sin\frac{\pi}{2}=2\\ x=\pi &\Rightarrow y=2\sin\pi=0 \end{aligned} \]
Thus the curve passes through the points
\[ (0,0),\quad \left(\frac{\pi}{2},2\right),\quad (\pi,0) \]
Plot these points and draw a smooth sine curve through them.
Hence, the required graph is shown above.
Graph Features:
- Amplitude = \(2\)
- Domain = \(0 \le x \le \pi\)
- Range = \(0 \le y \le 2\)
- Maximum value = \(2\)