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) to the peak (maximum) or trough (minimum) of the graph. It is calculated as half the distance between the maximum and minimum values.

Front

What is the period of a sine or cosine function?

Back

The period is the length of one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

Front

How do you determine the period of a transformed sine function?

Back

The period of a transformed sine function y = a sin(bx) is calculated as 2π/|b|. The value of b affects the frequency of the wave.

Front

What is the phase shift in a sine or cosine function?

Back

The phase shift is the horizontal shift left or right for the graph of a sine or cosine function. It is determined by the value of c in the function y = a sin(b(x - c)).

Front

What is the vertical shift in a sine or cosine function?

Back

The vertical shift is the upward or downward movement of the graph of a sine or cosine function. It is determined by the value of d in the function y = a sin(bx) + d.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are related through the identity sin(x) = cos(π/2 - x). They are phase-shifted versions of each other.

Front

What is the effect of changing the amplitude on the graph of a sine function?

Back

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude results in taller peaks and deeper troughs.

Front

What is the effect of changing the period on the graph of a sine function?

Back

Changing the period affects the width of the graph. A shorter period results in more cycles within a given interval, making the graph appear more compressed.