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How do you find the amplitude, period, phase shift for #y=cos(1/2x)#?

Answer 1

Carter Anderson

#y = cos (x/2)# Amplitude --> #+- 1# Period --> #2(2pi) = 4pi# Phase shift --> 0

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Answer 2

Emery Adkins

To find the amplitude, period, and phase shift for the function ( y = \cos\left(\frac{1}{2}x\right) ), you can use the following relationships:

Amplitude: The amplitude of ( \cos(ax) ) is always 1.
Period: The period of ( \cos(ax) ) is ( \frac{2\pi}{|a|} ).
Phase Shift: For ( \cos(ax + b) ), the phase shift is ( -\frac{b}{a} ).

In the given function ( y = \cos\left(\frac{1}{2}x\right) ):

The amplitude is 1.
The period is ( \frac{2\pi}{\left|\frac{1}{2}\right|} = 4\pi ).
There is no phase shift as the function is of the form ( \cos\left(\frac{1}{2}x\right) ).

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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.