Sine and Cosine Graphs

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude represents half the distance between the maximum and minimum values of the graph.

Front

How is the period of a sine or cosine graph calculated?

Back

The period can be found using the formula 2π/B, where B is the frequency.

Front

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

Back

y = 6sin(8x) because the frequency B is 8.

Front

What is the equation of the graph if the amplitude is 3, the phase shift is 0, and the vertical shift is -4?

Back

y = -3 cos x - 4.

Front

What is the period of a sine function with a frequency of 2?

Back

The period is π because the formula is 2π/B.

Front

Define the term 'frequency' in the context of sine and cosine graphs.

Back

Frequency refers to the number of cycles a sine or cosine graph completes in a unit interval.

Front

What does a vertical shift in a sine or cosine graph do?

Back

A vertical shift moves the graph up or down without affecting its shape.

Front

How does changing the amplitude affect the graph of a sine function?

Back

Changing the amplitude stretches or compresses the graph vertically.

Front

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

Back

The maximum value is 4, which is the amplitude.

Front

What is the minimum value of the function y = -2cos(x)?

Back

The minimum value is -2, which is the amplitude in the negative direction.