Question

predict #3
if we changed the 3 to a 1 in the equation, what would happen to
the graph?
share with class
$y = 2\sin 3(x - \pi)+1$

Explanation:

Step1: Recall the formula for the period of a sine function

The general form of a sine function is \(y = A\sin(B(x - C))+D\), and its period is \(T=\frac{2\pi}{|B|}\).

Step2: Calculate the original period

For the function \(y = 2\sin(3(x-\pi)) + 1\), \(B = 3\). Using the period formula \(T=\frac{2\pi}{|B|}\), we have \(T_{1}=\frac{2\pi}{3}\).

Step3: Calculate the new period

If we change \(B = 3\) to \(B = 1\), then using the period formula \(T=\frac{2\pi}{|B|}\), we get \(T_{2}=\frac{2\pi}{1}=2\pi\).

Answer:

The period of the sine - wave graph would increase. The original period was \(\frac{2\pi}{3}\), and after changing the \(3\) to a \(1\), the new period is \(2\pi\). So the graph would be stretched horizontally.