Write the sine function with an amplitude of 1/4, a period of 3pi, phase shift of pi4 to the right, and a vertical shift of 4 units down.
To write the sine function with the given amplitude, period, phase shift, and vertical shift, you can use the general form of a sine function:
y = A*sin(B(x - C)) + D
where:
A is the amplitude,
B is the frequency,
C is the phase shift, and
D is the vertical shift.
Given:
Amplitude (A) = 1/4
Period (T) = 3π
Phase shift (C) = π/4 to the right
Vertical shift (D) = 4 units down
Let's plug in these values into the general form equation:
y = (1/4)*sin(B(x - π/4)) + 4
The next step is to determine the value of B. To find the frequency (B), we can use the formula:
B = (2π) / T
where T is the period. Substituting the given period (3π) into the formula, we get:
B = (2π) / (3π) = 2/3
Now we can substitute this value back into the equation:
y = (1/4)*sin((2/3)(x - π/4)) + 4
Therefore, the sine function with an amplitude of 1/4, a period of 3π, a phase shift of π/4 to the right, and a vertical shift of 4 units down is:
y = (1/4)*sin((2/3)(x - π/4)) + 4