Write the equation of the trigonometric graph. Amplitude is 4, Midline is 1, Period is 5 pi.

Answer 1

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