Problem 99
Question
Determine the amplitude and period of \(y=3 \sin \frac{1}{2} x\) Then graph the function for \(0 \leq x \leq 4 \pi\)
Step-by-Step Solution
Verified Answer
The amplitude of the function \(y=3 \sin \frac{1}{2} x\) is 3, and the period is \(4\pi\).
1Step 1: Determine the Amplitude
The amplitude of a sine function is given by the absolute value of the coefficient of the sine term. In this case, it is |3| = 3.
2Step 2: Determine the Period
The period of a trigonometric function is given by the formula \(2\pi / |B|\), where B is the coefficient of x in the sine function. Here, \(B = \frac{1}{2}\). So the period of the function is \(2\pi / \frac{1}{2} = 4\pi\).
3Step 3: Graph the Function
Plot the function \(y = 3 \sin \frac{1}{2} x\), which has the amplitude as 3 and period as \(4\pi\), for the interval \(0 \leq x \leq 4 \pi\). Also plot several points for each quarter period.
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