Can I get some help please? Thanks

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3 Answers
Sep 22, 2017

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

Sep 22, 2017

"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

Sep 22, 2017

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