What is the amplitude, period and the phase shift of #y= 4 sin(theta/2)#?

1 Answer
Trevor Ryan.
Dec 15, 2015

Amplitude, #A=4#, Period , #T=(2pi)/(1/2)=4pi#, Phase shift , #theta = 0#

Explanation:

For any general sine graph of form #y=Asin(Bx+theta)#,

#A# is the amplitude and represents the maximum vertical displacement from the equilibrium position.
The period represents the number of units on the x-axis taken for 1 complete cycle of the graph to pass and is given by #T=(2pi)/B#.
#theta# represents the phase angle shift and is the number of units on the x-axis (or in this case on the #theta# axis, that the graph is displaced horizontally from the origin as intercept.

So in this case, #A=4#, #T=(2pi)/(1/2)=4pi#, #theta = 0#.

Graphically :

graph{4sin(x/2) [-11.25, 11.25, -5.625, 5.625]}

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