Question

The pistons in an automobile engine move up and down in the cylinders. If t is in milliseconds, the distance from the top of the piston to the top of the cylinder is given in centimeters by D=7+6 sin (4m)

(a) identify the amplitude, period and frequency of function

(b) Find the largest and the smallest clearance between the piston and the top of the cylinder.

Answer 1

(a) Amplitude $A=6.$

Period $P=\frac{2\pi}{4}=\frac{\pi}{2}.$

Frequency $f=\frac{2\pi}{P}=4.$

(b) Largest distance: $7+6=13$ cm.

Smallest distance: $7-6=1$ cm.