Question

Write a sine equation that has a period of
pi, amplitude of 3 and vertical shift down 7.

Answer 1

f(x) = 3sin(2x) - 7

Explanation:

The general equation for sine function is,

f(x) = Asin(B(x - C)) + D

C controls the horizontal shift so it is zero

C = 0,

A controls the amplitude,

A = 3

D is the vertical shift,

Since the shift is downwards, we get -7

D = -7,

B Controls the period,

Now, period = 2pi/B

So, for a period of pi,

pi = 2pi/B

B = 2.

So, we have the equation,

f(x) = 3sin(2x) + 7