Questions: Find the period and amplitude y=-3 sin (π/3 x)

Transcript text: Find the period and amplitude \[ y=-3 \sin \left(\frac{\pi}{3} x\right) \]

Solution

Solution Steps

Step 1: Determine the Amplitude

The amplitude of the function \( y = -3 \sin \left(\frac{\pi}{3} x\right) \) is given by the absolute value of the coefficient \( a \). Here, \( a = -3 \), so the amplitude is: \[ \text{Amplitude} = |a| = 3 \]

Step 2: Calculate the Period

The period of the sine function is calculated using the formula \( \frac{2\pi}{b} \), where \( b \) is the coefficient of \( x \) in the sine function. In this case, \( b = \frac{\pi}{3} \). Therefore, the period is: \[ \text{Period} = \frac{2\pi}{\frac{\pi}{3}} = 6 \]

Final Answer

The amplitude is \( 3 \) and the period is \( 6 \). Thus, the final answers are: \[ \boxed{\text{Amplitude} = 3} \] \[ \boxed{\text{Period} = 6} \]

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