Sine and Cosine Graphs

Front

What is the sine function?

Back

The sine function, denoted as sin(x), is a periodic function that describes the y-coordinate of a point on the unit circle as it rotates around the origin. It has a range of [-1, 1] and a period of 2π.

Front

What is the cosine function?

Back

The cosine function, denoted as cos(x), is a periodic function that describes the x-coordinate of a point on the unit circle as it rotates around the origin. It has a range of [-1, 1] and a period of 2π.

Front

What is the amplitude of a sine or cosine function?

Back

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

Front

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

Back

The period of a sine or cosine function is calculated using the formula: Period = 2π / |b|, where b is the coefficient of x in the function y = a sin(bx) or y = a cos(bx).

Front

What is the equation of a sine function with an amplitude of 3 and a period of π?

Back

y = 3 sin(2x) (since the period is π, b = 2).

Front

What is the equation of a cosine function with an amplitude of 5 and a period of 2π?

Back

y = 5 cos(x) (since the period is 2π, b = 1).

Front

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

Back

The phase shift is π/2 to the right.

Front

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

Back

The vertical shift is 3 units upward.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. Specifically, sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2).

Front

What is the maximum value of the function y = 4sin(x)?

Back

The maximum value is 4, which occurs when sin(x) = 1.