Question

The graph of a sinusoidal function intersects its midline at (0,−3)and then has a maximum point at (2,-1.5). Write the formula of the function, where x is entered in radians. f(x)= Please answer fast

1. thuthuy
The sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) – 3.

### How to derive a sinusoidal function

In this question we must derive a sinusoidal function based on two given points. Sinusoidal functions are periodic functions that uses trigonometric functions and have the following form:
y = A · cos (2π · x/T) + B      (1)
Where:
• A – Amplitude
• T – Period
• B – Vertical midpoint
The horizontal distance between the midline and the maximum point is equal to a quarter of the period. Hence,
T = 4 · (2 – 0)
T = 8
The vertical midpoint and amplitude of the sinusoidal function are now calculated:
Vertical midpoint
B = – 3
Amplitude
A = – 1.5 – (- 3)
A = 1.5
Then, the sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) – 3.