properties of a sin function

What does parameter a determine?

The amplitude

What is the greatest value of parameter a?

a

What is the lowest value of parameter a?

-a

What is the range of parameter a?

2a

What is the key rule for changing the parameter a?

If you increase a, the wave gets taller. If you decrease a, the wave gets flatter. Changing a only changes how low/high the humps are

What does parameter b determine?

Frequency

What is the formula for the period of a sin function?

T = 2pi/b

What happens when b is large?

The wave is very fast. The period becomes smaller

What happens when b is small?

The wave is very slow. The period becomes larger

How is the parameter b and the zeros of a function related?

If b is larger, the waves are suished together, meaning you will see more zeros on a fixed interval

When do the zeros of a sin function occur?

Whenever the “inside” of the sine function equals a multitude of pi

What are the zeros for sin(x)

0, pi, 2pi

What are the zeros for sin(bx)

0, pi/b, 2pi/b

What is the distance between two consecutive zeros equal to?

It is equal to exactly half of a period; pi/b

as b gets bigger, the distance between the two consecutive zeros…

gets smaller