Radian and degree | Unit circle definition of trig functions | Trigonometry | Khan Academy

TL;DR

An explanation of radians and degrees, including their definitions and conversion formulas.

Transcript

Welcome to the presentation on radians and degrees. So you all are probably already reasonably familiar with the concept of degrees. I think in our angles models we actually drill you through a bunch of problems. You're probably familiar that a right angle is 90 degrees. Or half a right angle -- 45 degrees. And you're also probably familiar with th... Read More

Key Insights

• ⚾ Radians measure angles based on the length of the arc they subtend, while degrees are based on a division of a circle into 360 parts.
• ⭕ The conversion between radians and degrees can be derived from the relationships between the circumference of a circle and the length of the radius.
• 🛟 Radians are the mathematical standard for measuring angles, while degrees are more commonly used in everyday life.
• 💨 The conversion formulas provide a way to easily switch between radians and degrees in calculations.

Questions & Answers

Q: What is a radian and how is it related to a circle?

A radian is the angle that subtends an arc with the same length as the radius of a circle. It is closely related to a circle because 2 pi radians form a complete circle.

Q: How many radians are there in a circle?

There are 2 pi radians in a circle. This can be derived from the fact that the circumference of a circle is 2 pi times the radius.

Q: What is the conversion formula between radians and degrees?

The conversion formula is 1 radian = 180/pi degrees. This can be obtained by setting up an equation between the number of radians in a circle (2 pi) and the number of degrees in a circle (360).

Q: How do you convert degrees to radians?

To convert degrees to radians, you can use the formula: radians = degrees * (pi/180). Multiply the given number of degrees by pi/180 to get the equivalent in radians.

Summary & Key Takeaways

• Radians are a unit of measurement for angles, defined as the angle that subtends an arc with the same length as the radius.

• There are 2 pi radians in a circle, which is equal to 360 degrees.

• The conversion formulas are: 1 radian = 180/pi degrees and 1 degree = pi/180 radians.