Given the function , what are its amplitude and period?
A
Amplitude: , Period:
B
Amplitude: , Period:
C
Amplitude: , Period:
D
Amplitude: , Period:
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1
Identify the general form of the sine function: \(y = A \cdot \sin(Bx)\), where \(A\) is the amplitude and \(B\) affects the period.
Recall that the amplitude of a sine function is the absolute value of the coefficient \(A\) in front of the sine, so amplitude \(= |3| = 3\).
Recall the formula for the period of a sine function: \(\text{Period} = \frac{2\pi}{B}\), where \(B\) is the coefficient of \(x\) inside the sine function.
In the given function \(y = 3 \cdot \sin(2x)\), identify \(B = 2\).
Calculate the period using the formula: \(\text{Period} = \frac{2\pi}{2} = \pi\).