Write a sine function that has a midline of y, equals, 2, commay=2, an amplitude of 5 and a period of start fraction, 7, divided by, 4, end fraction 47 .
Question
Write a sine function that has a midline of , an amplitude of 5, and a period of .
Solution
The general form of a sine function is y = A sin(B(x - C)) + D, where:
- A is the amplitude
- B is the frequency
- C is the phase shift
- D is the vertical shift (midline)
Given that the midline is y = 2, the amplitude is 5, and the period is 7/4, we can substitute these values into the general form.
The period of a sine function is given by (2π) / B. So, B = (2π) / period. Substituting the given period of 7/4, we get B = (2π) / (7/4) = 8π/7.
Therefore, the sine function that meets the given conditions is:
y = 5 sin((8π/7)x) + 2
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