# Radians

10 videos

3 skills

Most people know that you can measure angles with degrees, but only exceptionally worldly people know that radians can be an exciting alternative. As you'll see, degrees are somewhat arbitrary (if we lived on a planet that took 600 days to orbit its star, we'd probably have 600 degrees in a full revolution). Radians are pure. Seriously, they are measuring the angle in terms of how long the arc that subtends them is (measured in radiuseseses). If that makes no sense, imagine measuring a bridge with car lengths. If that still doesn't make sense, watch this tutorial!

### Introduction to radians

VIDEO
10:51 minutes

Understanding the definition and motivation for radians and the relationship between radians and degrees

### Rotation by radians and quadrants

VIDEO
3:51 minutes

### Arc length as fraction of circumference

VIDEO
2:59 minutes

### Radians on the unit circle

PRACTICE PROBLEMS

A radian is a unit of angle measure, and it has a special relationship with arc length.

### Finding arc length from radian angle measure

VIDEO
2:39 minutes

### Ratio between concentric arcs

VIDEO
3:15 minutes

### Example: Radian measure and arc length

VIDEO
3:30 minutes

Worked example that thinks about the relationship between an arc length and the angle that is subtended by the arc.

### Radians and arc length

PRACTICE PROBLEMS

### Example: Converting degrees to radians

VIDEO
7:02 minutes

Worked example to help understand how we convert radians to degrees

### Example: Converting radians to degrees

VIDEO
3:20 minutes

Worked example showing how to convert radians to degrees

### Radian and degree conversion practice

VIDEO
7:12 minutes

A little practice converting between radians and degrees and vice versa

### Degrees to radians

PRACTICE PROBLEMS

### Radians and degrees

VIDEO
9:55 minutes

What a radian is. Converting radians to degrees and vice versa.