Question

Describe how the graph of each function is related to a basic trigonometric graph. Then, graph two periods.

1. y=0.5 cos(3x) Description:

2. y=-2 sin(2πx/3) Description:

3. y=4 sin(3πx)-2 Description:

Answer 1

QUESTION 1

The given trigonometric function is

`y=0.5\cos(3x)`

The amplitude of this function is 0.5 while the amplitude of the parent function
`y=\cos(x)` is 1.

The period of this function is
`(2\pi)/(3)` while the parent function is
`\2pi`

This function will complete two periods on the interval
`[0,(4\pi)/(3)]`

We plot some few points as shown on the graph and draw our curve through it.

QUESTION 2

The given function is

`y=-2\sin((2\pi)/(3)x)`

This function has a period of 3 while the corresponding basic function,
`y=\sin(x)` has a period of
`2\pi`

The amplitude of this function is 2 while that of the corresponding basic function is 1.

This function is reflected in the x-axis because of the negative a value.

We plot some few points and draw the graph as shown in the graph

QUESTION 3

The given function is

`y=4\sin(3\pi x)-2`

This function has an amplitude of 4 as compared to the amplitude of the basic sine which is 1.

It has a period of
`(2)/(3)` and shifted vertically 2 units down.

We plot some few points as shown in the graph and draw our graph through.