Question

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)

Accepted Answer

Identify the general form of the sine function: $$y = A \sin(Bx - C)$$, where $$A is $$the amplitude, $$B$$ affects the period, and $$C$$ relates to the phase shift. Find the amplitude by taking the absolute value of the coefficient in front of the sine function: $$	ext{Amplitude} = |A| = |-3|. $$Calculate the period using the formula $$	ext{Period} = \frac{2\pi}{|B|}. $$Here, $$B is $$the coefficient of $$x$$ inside the sine function, which is $$\frac{\pi}{3}. $$Determine the phase shift using the formula $$	ext{Phase shift} = \frac{C}{B}$$, where $$C is $$the constant subtracted inside the sine function (note the sign inside the parentheses). In this case, $$C = 3\pi$$ and $$B = \frac{\pi}{3}. To $$graph one period of the function, start at the phase shift on the x-axis, then plot points at intervals of $$\frac{	ext{Period}}{4} to $$capture key points of the sine wave (maximum, zero crossing, minimum, zero crossing), and use the amplitude to determine the y-values.

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)

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Key Concepts

Amplitude of a Sine Function

Period of a Sine Function

Phase Shift of a Sine Function