A sine function is transformed such that it has a single x-intercept in the interval [0,pi], a period of pi, and a y-intercept of 3.

a) Determine an equation for a function that satisfies the properties given.

Equation form: y=asin[k(x-d)]+c

I just want to know how I can derive the amplitude and vertical displacement from the given properties. I know 'k' is 2pi/pi, which is 2. But I don't know how to get the rest of the variables of the equation.

Question

A sine function is transformed such that it has a single x-intercept in the interval [0,pi], a period of pi, and a y-intercept of 3.

a) Determine an equation for a function that satisfies the properties given.

Equation form: y=asin[k(x-d)]+c

I just want to know how I can derive the amplitude and vertical displacement from the given properties. I know 'k' is 2pi/pi, which is 2. But I don't know how to get the rest of the variables of the equation.