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:

$d^2=\frac{985}{4}\Rightarrow d\approx15.69$

*t = 1:

$d^2=\frac{637}{4}\Rightarrow d\approx12.62$

*t = 2:

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

*t = 3:

$d^2=\frac{289}{4}\Rightarrow d=8.5$

*t = 4:

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

*t = 5:

$d^2=\frac{367}{4}\Rightarrow d\approx12.62$

*t = 6:

$d^2=\frac{985}{4}\Rightarrow d\approx15.69$

*t = 7:

$d^2=\frac{1333}{4}\Rightarrow d\approx18.26$

*t = 8:

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

*t = 9:

$d^2=\frac{1681}{4}\Rightarrow d=20.5$

*t = 10:

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

*t = 11:

$d^2=\frac{1333}{4}\Rightarrow d\approx18.26$

*t = 12:

$d^2=\frac{985}{4}\Rightarrow d\approx15.69$