Write an equation of sin with amplitude = 2, period = 2pi, and vertical shift = 5

So where is your attempt to do these?

To write an equation of a sine function with the given amplitude, period, and vertical shift, we need to know the general form of the equation for a sine function. The general form of a sine function is:

y = A*sin(Bx - C) + D

Where:
A is the amplitude of the function.
B is the coefficient that determines the period.
C is a phase shift (horizontal shift) of the function.
D is the vertical shift of the function.

Given the information that the amplitude is 2, the period is 2π, and the vertical shift is 5, we can substitute these values into the equation:

y = 2*sin(Bx - C) + 5

To determine the values of B and C, we can use the period of the function. The period of a sine function is given by the formula:

Period = 2π/B

In this case, the period is 2π, so we can set up the equation:

2π = 2π/B

Simplifying this equation, we find that B = 1.

Now we can substitute the value of B into our equation:

y = 2*sin(x - C) + 5

Next, we need to determine the phase shift, which is given by the formula:

Phase Shift = C/B

Since B is 1, the phase shift is C.

In this case, the period is 2π, which means the function completes one full period in the interval [0, 2π]. Since we want the function to start at x = 0, there is no phase shift. Therefore, C = 0.

Substituting this value into our equation, we obtain the final equation:

y = 2*sin(x) + 5

Thus, the equation of the sine function with an amplitude of 2, a period of 2π, and a vertical shift of 5 is y = 2*sin(x) + 5.