Problem 14 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the period and amplitude. $$y=-3 \sin \frac{x}{3}$$

Step-by-Step Solution

Answer

The amplitude is 3 and the period is \(6\pi\)

Step 1: Identify the amplitude

The amplitude of a sinusoidal function given by \(y = a \sin(bx)\) is the absolute value of 'a'. In this case, the amplitude would be \( |-3| = 3 \)

Step 2: Calculate the period

The period of the function can be calculated using the value 'b' from the general form of the sinusoidal function. The formula for the period is \(2\pi / |b|\). So, for this exercise, the period would be \(2\pi / |1/3| = 6\pi\)