Learning Objectives:

__Math Tutoring on Radian Measure and Application__

A **Radian** is based on the radius of a circle. One **Radian** is the angle created by bending the radius length around the arc of a circle. Because a Radian is based on an actual part of the circle rather than an arbitrary division, it is a much more natural unit of angle measure for upper-level mathematics.

The circumference of a circle is **2π Radians**. So it becomes 2π radians = 360 degrees.

In Math Tutoring, to convert radians to degrees, multiply a radian measure by **180°/π** and simplify.

The **Length Of An Arc** on a circle depends on both the angle of rotation and the radius length of the circle. We know that, a **Radian** is the measure of an angle that cuts off an arc the same length as the radius. So that a half-rotation is π radians, so the length of the half-circle would be π radius length.

On the other hand, the length **‘s’** of the arc intercepted on a circle of radius **‘r’** by a central angle of measure **‘θ’** radians is given by the product of the radius and the radian measure of the angle. So **s=rθ**.

One of the major application of Radian is the measurement of **Angular Velocity**. The measure of how fast a central angle is changing is called **Angular Velocity**, **ω**. So **ω=θ/t**. where **‘θ’** is the measure of the central angle at time **‘t’**. θ must be in radians and **ω(omega)** is expressed in radians per unit of time.

We know that the length **‘s’**, of an intercepted arc on a circle with radius **‘r’** by a central angle **‘θ’** is given by **s=rθ**. So the **Linear Speed Around a Circle** is

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**Hook Questions:**

*1. **What is Radian and how it is measured?*

*2. **Deduce the relation Radian and Degrees.*

*3. **What is Angular Velocity and how it is measured?*

*4. **How is Linear Speed around a Circle measured? *

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