Q:

Find an equation for a sinusoidal function that has period 360°, amplitude 1, and contains the point (180°,0). Write your answer in the form f(x)=Asin(Bx+C)+D, where A, B, C, and D are real numbers.

Accepted Solution

A:
The answer is:
 f(x) = 1*Sin(1*x + k*π).
 It must be remembered that:
 360°= 2π.
 180° = π.
 Therefore we see that:
 A = 1, where A represents the amplitude.
 B is equal to (2π / T) and T is the period of oscillation.
 If B = 1 then T = 2pi = 360 ° as requested.
 C is the phase.
 In the required equation C = kπ, where k is any whole number.
 D = 0
 Below is a graph of the equation:
 f (x) = 1sin (x + kπ) with k = 2 for this case.
 It can be seen that indeed the equation satisfied all the requirements of the problem