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How do you find the amplitude and period for #s = 1/2 cos (pit - 8)#?

Answer 1

The amplitude is the number in front of your #cos# which is #1/2#; the period is given considering the number in front of #t# which is #pi# as: #period=(2pi)/pi=2#

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Answer 2

Abigail Armstrong

To find the amplitude and period of the function ( s = \frac{1}{2} \cos ( \pi t - 8 ) ), we first identify the coefficient of the cosine function as the amplitude, and the coefficient of ( t ) inside the parentheses of the cosine function as the frequency. The period of the function is then determined by dividing ( 2\pi ) by the frequency.

For the given function ( s = \frac{1}{2} \cos ( \pi t - 8 ) ), the amplitude is ( \frac{1}{2} ). The coefficient of ( t ) inside the parentheses of the cosine function is ( \pi ). Therefore, the frequency is ( \pi ), and the period ( T ) is given by:

[ T = \frac{2\pi}{\pi} = 2 ]

So, the amplitude of the function is ( \frac{1}{2} ), and the period is ( 2 ) 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.