Question

Write an equation of the sine function.
amplitude: 4, period: pi, phase shift: -1/6 pi, vertical shift: -1

Answer 1

@ejune420 What do you mean by amplitude here?
sin can take maximum value of +1

Answer 2

The general equation is as follows:
\[y=A \sin (Bx+C)+D\]
where:
amplitude is |A|
period T = 2 pi/B
phase shift = C/B
'y' shift = D

In your question the term A in the general equation can be either 4 or -4.
\[T=\pi=\frac{2 \pi}{B}\ .........(1)\]
You need to solve equation (1) to find B.
\[phase\ shift=-\frac{1}{6} \pi=\frac{C}{B}\ .........(2)\]
You need to substitute the value for B into equation (2) and then solve to find C.
\[D=-1\]