Question

The height h in inches of pistons 1 and 2 in an automobile engine can be modeled by h1 = 3.75sin(733t) + 7.5 and h2 = 3.75sin[733(t+ 4π/3)] + 7.5 where t is measured in seconds. How often are these two pistons at the same height? Show work please.

Answer 1

you would want:

3.75sin(733t) + 7.5 = 3.75sin[733(t+ 4π/3)] + 7.5
divide each term by 3.75, (how convenient ?)

sin(733t) + 2 = sin[733(t+ 4π/3)] + 2
sin(733t) = sin[733(t+ 4π/3)]
this can only be true if

733t = 733(t + 4π/3) OR 733(t+4π/3) = π - 733t
divide by 733
t = t + 4π/3 , not possible!

or
733(t+4π/3) = π - 733t
733t + 2932π/3 = π - 733t
1466t = -2929/3 π
t = appr -2.092 ---> this works in the original equation

period of each curve = 2π/733 = appr .00857