For the function y 5sin 2x pi2 find the amplitude period a

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

Solution

y= 5 sin(2x   + 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 function

Amplitude ,A = 5

Period =2pi/2=pi

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