SOLUTION: I need help with this: Find the value of k for which {{{y = 1/k}}} sin k x has a period of {{{4pi}}}

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Question 991918: I need help with this: Find the value of k for which y+=+1%2Fk sin k x has a period of 4pi
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe your answer is that k = 1/2.

here's why.

the equation is y = 1/k * sin(kx)

k is the frequency.

the period is equal to 2pi / frequency.

the period is 4pi.

you get 4pi = 2pi / k

solve for k to get k = 2pi / 4pi which is equal to 1/2.

a wrinkle in this problem is that k is also involved in the amplitude.

disregard that for purposes of solving the problem since the frequency and the period are you main interests.

your equation becomes y = 1/(1/2) * sin (1/2 * x).

the graph of that equation is shown below:

$$$

note that the amplitude is 2.

normally it is 1, but 1/(1/2) is equal to 2.

the k affected the amplitude as well as the period.