## Angular Positions of a clock

**1) What is the angular position in radians of the minute hand of a clock at 5:00?**

To start this problem, you have to pay close attention to what they are asking: “the minute hand”.

It is assumed that from 9 to 3 on the clock would make a 180 **°** angle.

The minute hands points at the **“12″ at 5:00**. The minute hand pointing at “12″ yields **90 °**relative to the previously establish model of 180

**°**.

We know the **angular position** of the minute hand at 5:00 is **90 °**. All we have to do is convert degrees to radians. To do this:

We multiply the degrees by** π/180**

90 × π/180= **90****π/180**

90π/180 **= 1.57 rad or radians**

θ **=1.57 rad**

**2) What is the angular position in radians of the minute hand of a clock at 6:15?**

Since the minute hand is on 3 the angle is zero.

0 × π/180= **0π/180**

0/180 = **0 rad or radians**

θ =**0 rad**

**3) What is the angular position in radians of the minute hand of a clock at 2:55?**

This problem is a little trickier because the angle is not as clear cut as the other ones. To find the angle, we just need to do a little thinking. A whole circle is 360 **°**. There are 12 numbers in an analog clock. If you divide 360 by 12, you would get 30. Each number would represent 30**°**. At 2:55, the minute hand would stop at “11″. This is basically 90 **°** with an added 30 degrees, which would equal to 120 **°**.

120 × π/180= **120π/180**

376.99/180 = **2.09 rad or radians**

θ =**2.09 rad**

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