Question

Write the equation of a sine function that has the following characteristics.

1
Amplitude: 4 Period: 7pi Phase shift:
1/5

Answer 1

`y=4\sin((2)/(7)x-(2)/(35))`

Explanation:

Period:
`7\pi=(2\pi)/(b)\rightarrow b=(2)/(7)`

Phase Shift:

`\displaystyle (c)/(b)=(1)/(5)\\\\\rightarrow(c)/((2)/(7))=(1)/(5)\\\\\rightarrow (2)/(7)=5c\\ \\\rightarrow (2)/(35)=c`

Final equation:

`y=4\sin((2)/(7)x-(2)/(35))`