Question

Can I get some help please? Thanks

Answer 1

Part a.

Please observe that the cosine function starts at the value of 4 at `x = 0`:

`4 = Acos(B(0))`

and then repeats the value of 4:

`4 = A cos(B(pi))`

Therefore, the period must be `pi`

We can double-check this by observing that it repeats the value of 4, again, `pi` units later.

Because the value of the function varies between 4 and -4, the amplitude must be 4.

End part a.

Part b.

By observation:

The maximum values occur at `0, pi, and 2pi`

The minimum values occur at `pi/2 and (3pi)/2`

The zeros occur at `pi/4, (3pi)/4, (5pi)/4, and (7pi)/4`

Answer 2

`"see explanation"`

Explanation:

`• " Amplitude is the distance from the "theta" axis to the"`
`"peak of the wave"`

`"from the origin "O to 4`

`rArr"amplitude "=4`

`• " period is the distance covered by 1 complete wave"`

`"from 1 point on the wave to the same point along the wave"`

`"consider the peak of 4 at the origin, then the next peak"`
`"of 4 occurs at "pi" on the "theta" axis"`

`rArr"period "=pi`

`"maximum values of + 4 at "theta=0,theta=pi,theta=2pi`

`"minimum values of - 4 at "theta=pi/2,theta=(3pi)/2`

`color(blue)"zeros"" are where the wave intersects the "theta" axis"`

`"zeros occur at "theta=pi/4,theta=(3pi)/4,theta=(5pi)/4,theta=(7pi)/4`

Answer 3

See below.

Explanation:

a.) The period is the distance from one peak to the next peak, or from one trough to the next trough. From the graph this can be seen as being from `theta = 0` to `theta = pi`;

So the period is `pi`

The amplitude is the distance from the horizontal axis to the top of a peak. From the graph this can be seen as 4:

So amplitude is 4:

b.)
Maximum value of 4 between `0<= theta <=2pi` are the peaks, this can be seen where:

`theta = 0`
`theta = pi`
`theta = 2pi`

Minimum value -4 between `0<= theta <=2pi` are the lowest part of the troughs. From graph these can be seen to occur at:

`theta = (pi)/2`

`theta = (3pi)/2`

The zeros occur where the curve cuts the horizontal axis. From graph these can be seen to occur at:

`theta = (pi)/4`

`theta = (3pi)/4`

`theta = (5pi)/4`

`theta = (7pi)/4`