Question

The graph of a sinusoidal function intersects its midline at (0,1) and has a minimum point at (7π/4,5). What is the formula of the function, where x is entered in radians?

A) f(x) = 5sin(x) + 1

B) f(x) = -5sin(x) + 1

C) f(x) = 5cos(x) + 1

D) f(x) = -5cos(x) + 1

Answer 1

The formula of the function is f(x) = 4sin(2(x - 7π/4)) + 1.

Step-by-step explanation:

The graph of a sinusoidal function intersects its midline at (0,1) and has a minimum point at (7π/4,5). To find the formula of the function, we need to determine the amplitude and the period.

Since the midline is at y = 1, the amplitude is the distance between the midline and the minimum point, which is 5 - 1 = 4.

The period can be found by calculating the distance between two consecutive minimum points. In this case, the minimum points occur at x = 7π/4 and x = 7π/4 + π. The difference between these two points is π, so the period is π.

The formula of the function is therefore f(x) = Amplitude * sin(2π/Period * (x - x-coordinate of the minimum point)) + midline. Plugging in the values, we get f(x) = 4sin(2(x - 7π/4)) + 1.