Write a cosine function that has an amplitude of 5, a midline of y=2 and a period of 3π.
The general form of a cosine function is given by:
y = A*cos(B(x - C)) + D
where A represents the amplitude, B represents the period and any horizontal shift, C represents any horizontal shift, and D represents the vertical shift.
In this case, we have:
Amplitude (A) = 5
Midline = y = 2 (which corresponds to a vertical shift of +2)
Period (B) = 3π
Plugging these values into the general form, we have:
y = 5*cos(B(x - C)) + 2
Now, since the period for cosine function is determined by 2π/B, we know that 3π = 2π/B. Solving for B:
3π = 2π/B
B = 2/3
Plugging this values into the equation, we have:
y = 5*cos((2/3)(x - C)) + 2
So, the cosine function with an amplitude of 5, a midline of y = 2, and a period of 3π is given by:
y = 5*cos((2/3)(x - C)) + 2