Certainly! Given the information provided, we can represent the sinusoidal function with the equation:
y = A sin(Bx - C) + D
where: A represents the amplitude, B represents the angular frequency, C represents the phase shift, D represents the vertical shift.
Using the given information, we can substitute the values into the equation:
Amplitude (A) = 6 units Period = 150°, which corresponds to 150°/360° = 5/12 of a full cycle. Since a full cycle is 2π radians, the angular frequency (B) can be calculated as B = 2π / (5/12) = 24π/5. Maximum at (2, 4) gives us the vertical shift (D) as 4.
Now, we need to find the phase shift (C). The maximum occurs at x = 2, which corresponds to an angle of 360°/12 * 2 = 60°. In radians, this is 60° * (π/180°) = π/3. Thus, the phase shift (C) is π/3.
Substituting the values into the equation, we get:
y = 6 sin((24π/5)x - π/3) + 4
Therefore, the equation representing the given sinusoidal function is:
y = 6 sin((24π/5)x - π/3) + 4