Sine and Cosine Graphs

Front

What is the period of a sine or cosine graph?

Back

The period is the distance along the x-axis for one complete cycle of the graph, calculated as 2π/B, where B is the frequency.

Front

How do you determine the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak, represented by the coefficient in front of the sine or cosine function.

Front

What is the general form of a sine function?

Back

The general form 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 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 period of the function y = 3 sin(2x)?

Back

The period is calculated as 2π/B, where B = 2, so the period is 2π/2 = π.

Front

What is the amplitude of the function y = -4 cos(x)?

Back

The amplitude is 4, as amplitude is always a positive value regardless of the sign of A.

Front

How does a horizontal shift affect the sine or cosine graph?

Back

A horizontal shift, represented by C in the function, moves the graph left or right along the x-axis.

Front

What is the vertical shift in the function y = sin(x) + 2?

Back

The vertical shift is 2, moving the entire graph up by 2 units.

Front

What is the effect of a negative coefficient in front of the cosine function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

How do you write the equation for a sine function with an amplitude of 5 and a period of π/2?

Back

The equation is y = 5 sin(4x), since the period is 2π/B, B = 4.