Final answer:
The equation for a cosine function with a maximum value of 1, a minimum value of -5, a phase shift of π/4 to the right, and a period of 2 is y = 3 cos(πx/2 - π/4) - 2.
Step-by-step explanation:
The equation for a cosine function with a maximum value of 1, a minimum value of -5, a phase shift of π/4 to the right, and a period of 2 can be written as:
y = A cos(Bx + C) + D
where:
- A is the amplitude (half the difference between the maximum and minimum values)
- B is the coefficient of x (related to the period)
- C is the phase shift
- D is the vertical shift
In this case, since the maximum value is 1 and the minimum value is -5, the amplitude is (1 - (-5))/2 = 3. The coefficient of x is 2π/(period) = 2π/2 = π. The phase shift is π/4 to the right, so C = -π/4. The vertical shift is (maximum + minimum)/2 = (1 + (-5))/2 = -2. Therefore, the equation becomes:
y = 3 cos(πx/2 - π/4) - 2