# Radians and Arc Length

### Geoffrey, Olivia, Melanie, Sara

## Arc Lengths

**Circumference of a Circle :**πd = 2πr

**Area of a Circle** : πr²

*** d = distance, r = radius ***

**Arc** : part of the circle between two points on the circle.

**Arc** **Length** : the length of the arc between two points on a circle

*** Fraction of the circumference ***

••• **Formula** : (measure of arc/360º) x 2πr •••

## What is the value of X?*Remember the measure of the intercepted arc is double the measure of the inscribed angle.* So the value of X is equal to 124÷2 = 162º | ## What is the value of X? *Remember the measure of the intercepted arc is equal to the measure of the central angle.* So the value of X is equal to 139º | ## What is the value of X? *Remember the measure of the intercepted arc is double the measure of the inscribed angle.* *Remember the measure of the intercepted arc is equal to the measure of the central angle.* So the value straight across from X is equal to 32º•2 = 64 So the value of X is equal to 64º÷2 = 32º |

## What is the value of X?

*Remember the measure of the intercepted arc is double the measure of the inscribed angle.*

So the value of X is equal to 124÷2 = 162º

## What is the value of X?

So the value of X is equal to 139º

## What is the value of X?

*Remember the measure of the intercepted arc is equal to the measure of the central angle.*

So the value straight across from X is equal to 32º•2 = 64

So the value of X is equal to 64º÷2 = 32º

## Find the values of the different arcs - Keep in the values of π

***** **Arc Length **Formula** : (measure of arc/360º) x 2πr** *****

**Arc AB**

- The angle is 105 so the distance across it is 105.
- Then divide (105÷360) which simplifies to (7/24).
- You then multiply. (7/24)(2) and add pi on the end of the number.
- The final answer : 7/12π

**Arc BC**

- The angle is 50º so the distance across it is 50º.
- Then divide (50÷360) which simplifies to (5/36).
- You then multiply (5/36)(2) and add pi on the end of the number.
- The final answer : 5/18π

**Arc ED**

- The angle is 120º so the distance across it is 120º.
- Then divide (120÷360) which simplifies to (1/3).
- You then multiply (1/3)(2) and add pi on the end of the number.
- The final answer : 2/3π

## Radians

## What is radian?

Radian is a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.

## Converting between degrees and radians

To convert radians to degrees multiply your given amount of radians by (180/π)

To convert degrees to radians multiply your given amount of degrees by (π/180)

- When you multiply the π can cancel out.
- Radian is usually represented by ∂ or π

Change degree to radian

45º

- (45 degrees) • (π radian/180 degrees)
- When you multiply the 2 degrees will cancel out since one is on the top and the other is on the bottom and are left with just radian.
- You end up with 45π/180 radian which can simplify to 4π radian

Change radian to degree

π/3 radians

- (π/3 radians) • (180 degrees/π radian)
- When you multiply the 2 radians will cancel out since one is on the top and the other is on the bottom and are left with just degrees.
- You end up with 180π/3 degrees which can simplify to 60πº