The equation h = 7 cos (pi/3 t) models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

Question

The equation   h = 7 cos (pi/3 t)  models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

anonymous · Answer

I have this so far am I right?
a.
h=7cos[(pi/3)t]
 h/7=cos[(pi/3)t]
 arccos(h/7)=πt/3
 t=3arccos(h/7)/π 

b.
h=1cm
 t=3arccos(1/7)/π≈1.36 sec
 ..
 h=3cm
 t=3arccos(3/7)/π≈1.08 sec
 ..
 h=5cm
 t=3arccos(5/7)/π≈0.74 sec

anonymous · Answer

Just find the iverse function to find t

anonymous · Answer

are my answers for a and b right?

campbell_st · Answer

yes they are

anonymous · Answer

how do you do that @him1618