Sine and Cosine Graphs

Front

What is the equation of a cosine graph with a vertical shift downwards?

Back

The equation can be expressed as y = A cos(Bx) + D, where D is the vertical shift. For example, y = -3 cos x - 4 has a vertical shift of -4.

Front

What is the period of a sine or cosine function?

Back

The period of a sine or cosine function is given by the formula T = 2π/|B|, where B is the coefficient of x in the function y = A sin(Bx) or y = A cos(Bx).

Front

How do you determine if a function is sine or cosine based on its graph?

Back

If the graph starts at its maximum or minimum value, it is a cosine function. If it starts at zero and goes up or down, it is a sine function.

Front

What is the equation of a sine graph with an amplitude of 2?

Back

The equation can be expressed as y = 2 sin(x), where the amplitude is the coefficient of the sine function.

Front

How does the coefficient of x affect the period of a sine or cosine function?

Back

The coefficient of x (B) affects the period. The period is calculated as T = 2π/|B|. A larger B results in a shorter period.

Front

What is the amplitude of the function y = -4 cos(3x)?

Back

The amplitude is the absolute value of the coefficient in front of the cosine function, which is 4.

Front

What is the vertical shift in the function y = 2 sin(x) + 3?

Back

The vertical shift is 3, which moves the graph up by 3 units.

Front

What is the equation of a cosine graph with a phase shift to the right?

Back

The equation can be expressed as y = A cos(B(x - C)), where C is the phase shift. For example, y = 2 cos(3(x - π/2)) has a phase shift of π/2 to the right.

Front

How do you find the maximum and minimum values of a cosine function?

Back

The maximum value is A + D and the minimum value is -A + D, where A is the amplitude and D is the vertical shift.

Front

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

Back

The period is T = 2π/|5| = 2π/5.