# Suppose theta(t) measures the angle between a clock's minute and hour hands where theta is in...

## Question:

Suppose {eq}\theta(t) {/eq} measures the angle between a clock's minute and hour hands where theta is in radians and {eq}t {/eq} is in hours. What is {eq}\theta'(t) {/eq} at {eq}3 {/eq} o' clock?

## Radians:

Radians are a unit of angle measurement. A complete rotation (i.e., {eq}360^\circ {/eq}) measures {eq}2\pi {/eq} radians.

The length of a circular arc measuring {eq}\theta {/eq} radians, on a circle of radius {eq}r {/eq}, is given by the formula {eq}s=r\theta {/eq}. This is a much simpler formula than the arc length formula that would be required if {eq}\theta {/eq} were measured in any unit other than radians.

## Answer and Explanation: 1

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The angle between the minute hand and the 12-o'-clock position {eq}t {/eq} hours after the hour is {eq}\theta_M(t)=2\pi t {/eq}, because the minute...

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#### Learn more about this topic:

Radian Measure: Definition & Formula

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Chapter 30 / Lesson 10
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Read the definition of a radian. Understand what a radian measure of an angle is, and learn how to find the radian measure using the radian formula. Discover how to convert a degree measure into a radian measure.