a cosine function that passes through the points (1/2,1) and (3/2,-3).
the equation is f(x)= 2cos(πx-π/2)-1
Maximum value: y=1
Minimum value: y=-3
Midline: y=-1
Identify phase shift
Phase shift: π/2
could you show how you found that using formulas
To find the phase shift, we need to use the general form of the cosine function:
f(x) = A * cos(Bx - C) + D
Given the equation f(x) = 2*cos(πx - π/2) - 1, we can see that:
A = 2
B = π
C = π/2
D = -1
The formula for phase shift is: phase shift = C / B
Plugging in the values, we get:
Phase shift = (π/2) / π
Phase shift = 1/2
Therefore, the phase shift is π/2 or 1/2 in decimal form.
Use phase shift and b to determine c. (phase shift = -c/b)
To determine the value of C using the phase shift, we can rearrange the formula:
Phase shift = -C / B
Given that the phase shift is 1/2 and B = π, we can plug in these values:
1/2 = -C / π
To solve for C, multiply both sides by π:
C = -π/2
Therefore, the value of C is -π/2.