Radian and degree conversion practice | Trigonometry | Khan Academy

TL;DR

Learn how to convert between radians and degrees using simple equations and unit analysis.

Transcript

Lets see if we can give ourselves a little bit of practice converting between radians and degrees and degrees and radians. And just as a review lets just remind ourselves the relationship and I always do this before I have to convert between the two. If I do one revolution of a circle how many radians is that going to be? Well we know one revolutio... Read More

Key Insights

• 🟰 One revolution of a circle is equal to 2π radians or 360 degrees.
• ✖️ Converting radians to degrees involves dividing by π and multiplying by 180.
• ✖️ Converting degrees to radians involves dividing by 180 and multiplying by π.
• ❓ The equation for converting radians to degrees is radians = (degrees/180) * π.
• ❓ The equation for converting degrees to radians is degrees = (radians/π) * 180.
• ⚾ The relationship between radians and degrees is based on the proportionality of 2π radians to 360 degrees.
• ❓ Understanding the conversion between radians and degrees is essential for trigonometric calculations.

Questions & Answers

Q: How many radians are in one revolution of a circle?

One revolution of a circle is equal to 2π radians.

Q: How do you convert radians to degrees?

To convert radians to degrees, divide the radians by π and multiply by 180.

Q: How do you convert degrees to radians?

To convert degrees to radians, divide the degrees by 180 and multiply by π.

Q: What is the equation for converting degrees to radians?

The equation is radians = (degrees/180) * π.

Q: What is the equation for converting radians to degrees?

The equation is degrees = (radians/π) * 180.

Summary & Key Takeaways

• One revolution of a circle is equal to 2π radians or 360 degrees.

• To convert radians to degrees, divide the radians by π and multiply by 180.

• To convert degrees to radians, divide the degrees by 180 and multiply by π.