Question

The graph of a sinusoidal function intersects its midline at (0, 1) and then has a maximum point at

Write the formula of the function, where is entered in radians.
f(x) =

Answer 1

f(x) = 4·sin(2/7x) +1

Explanation:

The sinusoidal function y = a·sin(kx) +b will have cross its midline at (0, b), and a peak value of (x, y) = (π/(2k), a+b). We can use these facts to find the values of a, k, and b for the sinusoidal function.

__

midline

(0, b) = (0, 1) ⇒ b = 1

peak value

(7π/4, 5) = (π/(2k), a+1)

This gives rise to two equations:

7π/4 = π/(2k)

k = π/(2(7π/4)) = 2/7

and

a+1 = 5

a = 4

equation

Using the found values for the parameters of the function, we have ...

f(x) = 4·sin(2/7x) +1