A minimum value of a sinusoidal Function is at (π4,3). The nearest maximum value to the right of this point is at (7π12,7). What is the equation of this function?

1 Answer
Dec 30, 2016

y(x)=2sin(3x5π4)+5

Explanation:

Let us write the generic sinusoidal function as:

y(x)=Asin(αx+β)+B

First we note that the value for the minimum is ym=3 while the maximum is for yM=7. From this we may derive:

A+B=3
A+B=7

and therefore:

A=2 and B=5

Then we note that a minimum of sinx occurs for x=π2 and the next maximum for x=π2, so we can derive:

αxm+β=π2
αxM+β=π2

or:

απ4+β=π2

α7π12+β=π2

subtracting the first equation from the second:

α(7π12π4)=π

so

α=171214=1712312=124=3

and

β=π234π=54π

Thus the sinusoidal function we are searching is:

y(x)=2sin(3x5π4)+5

graph{2sin(3x-(5pi)/4)+5 [-2.396, 2.604, 2, 8]}