for the function y5sin 4 pi2 find the amplitude period and

for the function y=5sin (4 + pi/2), find the amplitude, period and phase shift. draw the graph of y(x) over a one period interval and label all the maxima, minima and x-intercepts.

Solution

y=5 sin(4x + pi/2)

This is of the form y =A sin(Bx + C)

where A is the amplitude

Period=2pi/B

Phase shift=-C/B

Therefore for the given equation

AMplitude =5

Period=2pi/4=pi/2

Phase shift=-pi/2/4=-pi/8