Question

A clock has a radius of 6 inches. The center is 14.5 inches below the ceiling. Record the distance and write a sine or cosine equation. Complete the table and round your answers to the nearest hundredth.

Answer 1

We will have the following:

Equation:

`d^2=(14.5)^2+(6)^2-2(14.5)(6)\cos (\theta)`

Here we will have that each hour will be separated by 30°.

*We solve for each value of t:

*t = 0:

`d^2=(985)/(4)\Rightarrow d\approx15.69`

*t = 1:

`d^2=(637)/(4)\Rightarrow d\approx12.62`

*t = 2:

`d\approx\sqrt[]{95.56}\Rightarrow d\approx9.78`

*t = 3:

`d^2=(289)/(4)\Rightarrow d=8.5`

*t = 4:

`d\approx\sqrt[]{95.56}\Rightarrow d\approx9.78`

*t = 5:

`d^2=(367)/(4)\Rightarrow d\approx12.62`

*t = 6:

`d^2=(985)/(4)\Rightarrow d\approx15.69`

*t = 7:

`d^2=(1333)/(4)\Rightarrow d\approx18.26`

*t = 8:

`d\approx\sqrt[]{396.94}\Rightarrow d\approx19.92`

*t = 9:

`d^2=(1681)/(4)\Rightarrow d=20.5`

*t = 10:

`d\approx\sqrt[]{396.94}\Rightarrow d\approx19.92`

*t = 11:

`d^2=(1333)/(4)\Rightarrow d\approx18.26`

*t = 12:

`d^2=(985)/(4)\Rightarrow d\approx15.69`