Sine and Cosine Graphs

Front

What is the period of a sine or cosine graph?

Back

The period of a sine or cosine graph is the distance along the x-axis required for the function to complete one full cycle. It can be calculated using the formula: Period = 2π/B, where B is the coefficient of x in the function.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude of a sine or cosine function is the maximum distance from the midline (equilibrium position) of the graph to its peak (or trough). It is represented by the coefficient in front of the sine or cosine function.

Front

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

Back

A function is sine if it starts at the midline and goes up (e.g., y=sin(x)). A function is cosine if it starts at its maximum value (e.g., y=cos(x)).

Front

What is the equation for a sine function with an amplitude of 6 and a period of π/4?

Back

The equation is y = 6sin(8x). The period is calculated as 2π/B, so B = 8.

Front

What is the period of the function y=4cos(5x)?

Back

The period is 2π/5. This is calculated using the formula Period = 2π/B, where B = 5.

Front

What does the coefficient in front of the sine or cosine function represent?

Back

The coefficient represents the amplitude of the function, which indicates how far the graph stretches vertically from the midline.

Front

What is the general form of a sine function?

Back

The general form of a sine function is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form of a cosine function is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

How do you find the vertical shift of a sine or cosine function?

Back

The vertical shift is determined by the value of D in the general form of the function. If D is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of changing the value of B in the sine or cosine function?

Back

Changing the value of B affects the period of the function. A larger B results in a shorter period, while a smaller B results in a longer period.