Sine, Cosine, and Tangent Graphs

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is half the distance between the maximum and minimum values of the function.

Front

What is the period of a sine or cosine function?

Back

The period is the horizontal length required to complete one full cycle of the graph. For sine and cosine functions, the period is typically 2π.

Front

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

Back

The equation is y = 2 sin(x).

Front

How do you determine the period of a sine or cosine function from its equation?

Back

The period can be determined from the coefficient of x in the function's equation. For y = a sin(bx), the period is given by 2π/|b|.

Front

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

Back

The period is π, since b = 2 in the equation y = sin(bx).

Front

What is the parent function of the sine graph?

Back

The parent function of the sine graph is y = sin(x).

Front

What is the parent function of the cosine graph?

Back

The parent function of the cosine graph is y = cos(x).

Front

What is the tangent function's period?

Back

The period of the tangent function is π.

Front

Which of the following functions has a period of 2π: y = sin(x), y = cos(x), or y = tan(x)?

Back

Both y = sin(x) and y = cos(x) have a period of 2π, while y = tan(x) has a period of π.

Front

What is the phase shift in a trigonometric function?

Back

The phase shift is the horizontal shift left or right for periodic functions, determined by the value of c in the equation y = a sin(b(x - c)).