How do you complete this table? A clock has a radius of 8 inches.

Question

Picture the clock, with a radius of 8 inches, on a flat surface with the ceiling depicted as a horizontal line 10 inches above the center of the clock.  Measure the distance from the ceiling to the tip of the hour hand at each hour beginning at 12:00 (which is t=0).  For example, at t=0, d=2 inches.   Complete the table and round your answers to the nearest hundredth, if needed.  Then, write an equation using the sine or cosine function to determine how you solved the problem. 

 

   t   l    d   

  0   l   2

       l

       l

       l

       l

       l

 

Answer 1

the Cosine function will allow us to track the height of the tip of the hour hand as it moves around the circle

 

the height of the tip will equal 8 cos (30t)

 

this is true becasue the hour hand will move 1/12 of the circle each hour and 1/12 is 30 degrees

 

so our angle is 30 degrees  after one hour  and will increase by 30 every hour

 

the distance d = 10 - 8 cos(30t)  since the distance to the ceiling will change as the hour hand moves aroud the circle and will reach a maximum when the hour hand is a six oclock (180 degrees) at that point the distance formula will give us

 

d = 10 - 8(-1)  = 18

 

You should be able to substiture other values of t and see how the distance changes as the hour hand moves around the circle.

 

Good luck