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How do you find the period, amplitude and sketch #y=sin(x-pi)#?

Answer 1

Period= 2#pi# ;
Amplitude=1;
graph{sin(x-pi) [-10, 10, -5, 5]}

It is Simple!

Period: Period is the complete revolution of a wave completing crest and followed by trough. So, for this sine function , the period is 2 #pi#. Because, it becomes zero at first # #x#= pi#, and then completing one crest, becomes zero at # #x#= 2pi#. And, then completing one trough becomes zero # #x#= 3pi#. So, it had completed one revolutions , difference in #x# on both sides is #2pi#. Hence, the period is #2pi#.

Amplitude: Next, we want to that this function attains a maximum value of 1 at both sides of #x#-axis. So, for every wave like function (here, sine function), the general equation is #y=asin(z)#, where #a# is the amplitude. Here the amplitude is 1!.

Graph-Refer.: https://tutor.hix.ai(+x+%E2%88%92+%CF%80+)

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Answer 2

Delilah Aguilar

To find the period, amplitude, and sketch of ( y = \sin(x - \pi) ):

Period: The period of ( y = \sin(x - \pi) ) is the same as the standard sine function, which is ( 2\pi ).
Amplitude: The amplitude of ( y = \sin(x - \pi) ) is also the same as the standard sine function, which is 1.
Sketch: Start with the standard sine function ( y = \sin(x) ) and shift it to the right by ( \pi ) units. The graph will have the same shape as the standard sine curve, but it will be shifted to the right by ( \pi ) units.

Remember that the sine function has a range between -1 and 1, so the maximum value will be 1 and the minimum value will be -1. Therefore, the sketch will oscillate between these values but will be shifted to the right by ( \pi ) units.

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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.