Question 991918
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:


<img src = "http://theo.x10hosting.com/2015/092407.jpg" alt="$$$" </>


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.