# Thread: Finding The Vertical Translation

1. ## Finding The Vertical Translation

Hi there!

How would you solve for b and n in this question (I know how to solve for A):

A function with the rule
y=Asin(nt)+b has the range [2,8] and the period 2pi/3
Find A, b and n

Any help much appreciated!

2. ## Re: Finding The Vertical Translation

sin(x) has period $2\pi$ so sin(nt) will complete one full period when nt goes from 0 to $2\pi$. What is t when $nt= 2\pi$? What must n be so that will be equal to $2\pi/3$?

The smallest possible value for sin(x) is -1 so the smallest possible value for A sin(nt)+ b is -A+ b. The largest possible value for sin(x) is 1 so the largest possible value for A sin(nt)+ b is A+ b. Here you want the function to go from 2 to 8. That is, you want -A+ b= 2 and A+ b= 8.

3. ## Re: Finding The Vertical Translation

Thank you :-)