Sinusoidal Functions

Front

What is a sinusoidal function?

Back

A sinusoidal function is a mathematical function that describes a smooth, periodic oscillation. It can be represented by sine or cosine functions, such as y = sin(x) or y = cos(x).

Front

What is the general form of a sinusoidal function?

Back

The general form of a sinusoidal function is y = a sin(bx - c) + d or y = a cos(bx - c) + d, where 'a' is the amplitude, 'b' affects the period, 'c' is the phase shift, and 'd' is the vertical shift.

Front

How do you find the amplitude of a sinusoidal function?

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The amplitude of a sinusoidal function is the absolute value of 'a' in the equation y = a sin(bx - c) + d or y = a cos(bx - c) + d. It represents the maximum distance from the midline to the peak.

Front

What is the period of a sinusoidal function?

Back

The period of a sinusoidal function is the distance (in terms of x) it takes for the function to complete one full cycle. It can be calculated using the formula P = \frac{2\pi}{|b|}, where 'b' is the coefficient of x.

Front

What is the phase shift in a sinusoidal function?

Back

The phase shift of a sinusoidal function is the horizontal shift left or right in the graph. It is determined by the value of 'c' in the equation y = a sin(bx - c) + d or y = a cos(bx - c), calculated as \frac{c}{b}.

Front

What is the vertical shift in a sinusoidal function?

Back

The vertical shift of a sinusoidal function is the amount by which the graph is shifted up or down. It is represented by 'd' in the equation y = a sin(bx - c) + d or y = a cos(bx - c).

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How do you determine if a function is sine or cosine?

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To determine if a function is sine or cosine, observe the starting point of the graph. A sine function starts at the midline (0) and goes up, while a cosine function starts at its maximum value (a).

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What is the amplitude of the function y = 3sin(x)?

Back

The amplitude of the function y = 3sin(x) is 3, which is the absolute value of 'a' in the general form.

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What is the period of the function y = 2cos(4x)?

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The period of the function y = 2cos(4x) is \frac{2\pi}{4} = \frac{\pi}{2}.

Front

What is the phase shift of the function y = sin(2x - \pi)?

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The phase shift of the function y = sin(2x - \pi) is \frac{\pi}{2} to the right.