sinusoidal function amplitude of 1/4 units period 720 and maximum point of (0,3/4)
To find the equation of the sinusoidal function with an amplitude of 1/4 units, a period of 720, and a maximum point of (0, 3/4), we can use the standard form of the sinusoidal function:
y = A * sin(Bx + C) + D
Given:
A (amplitude) = 1/4
Period = 720
The formula to find B is:
B = 2π / period
B = 2π / 720
Simplifying this expression, we get:
B = π / 360
Since the maximum point is at (0, 3/4), D (vertical shift) can be found as the average of the maximum and minimum values:
D = (maximum + minimum) / 2
D = (3/4 + (-3/4)) / 2
D = 0/2
D = 0
With all of this information, the equation becomes:
y = (1/4) * sin((π/360)x)
The final equation for the sinusoidal function is:
y = (1/4) * sin((π/360)x)