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How do you graph and list the amplitude, period, phase shift for #y=2csc2theta#?

Answer 1

Abigail Armstrong

As below.

Standard form of equation is #y = A csc (Bx - C) + D#

#Amplitude = "None", " Period " = (2pi) / |B|, " Phase Shift "= (-C)/B, " Vertical Shift " = D#

Given equation is #y = 2 csc 2theta#

#Amplitude " A" = "None"#

#"Period " = (2pi) / |B| = (2pi) / 2 = pi#

#" Phase Shift, Vertical Shift = None"#

graph{2 csc(2x) [-10, 10, -5, 5]}

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Answer 2

Adam Aguirre

To graph the function ( y = 2\csc^2(\theta) ), follow these steps:

Graphing: Plot points on the graph by substituting various values of ( \theta ) into the equation.
Amplitude: The amplitude of the cosecant function is the absolute value of the coefficient in front of the function, which is ( 2 ) in this case.
Period: The period of the cosecant function is ( 2\pi ) radians. There is no change in period due to a coefficient in front of the function.
Phase Shift: There is no phase shift for the cosecant function in this form.

So, to summarize:

Amplitude: ( 2 )
Period: ( 2\pi ) radians
Phase Shift: No phase shift

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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.