Write the equation of the trigonometric graph. Amplitude is 4, Midline is 1, Period is 5 pi.
The equation of the trigonometric graph can be written in the form:
y = A*sin(B(x - C)) + D
where:
- A is the amplitude
- B is the frequency (or period)
- C is the phase shift
- D is the midline (or vertical shift)
Given that the amplitude (A) is 4, the midline (D) is 1, and the period (B) is 5pi, we can write the equation as:
y = 4*sin(5pi*(x - C)) + 1
Now, we need to determine the phase shift (C). The phase shift can be calculated using the formula:
C = (horizontal shift / period)
In this case, there is no horizontal shift, so C = 0.
The final equation of the trigonometric graph is:
y = 4*sin(5pi*x) + 1