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

Answer 1

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

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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Answer 2

Caroline Adams

Amplitude: 4 Period: 4π Phase Shift: 0

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.