Write a sine function that has a midline of y, equals, 3, commay=3, an amplitude of 5 and a period of start fraction, 7, pi, divided by, 2, end fraction
2
7π
.
The general form of a sine function is y = A*sin(Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
Given: amplitude A = 5, midline D = 3, period 2(pi)/B = (7pi)/2
Since the period is 2(pi)/B, we can set (7pi)/2 = 2(pi)/B and solve for B:
(7pi)/2 = 2(pi)/B
Cross-multiplying and simplifying:
7piB = 4pi
B = 4pi/(7pi)
B = 4/7
Now we have A = 5, B = 4/7, D = 3. The phase shift C is not given, so we will assume it is 0.
Therefore, the sine function is:
y = 5*sin((4/7)x) + 3