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#