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Degree to Radian Measure

Master degree to radian measure with interactive lessons and practice problems! Designed for students like you!

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Degree to Radian Measure

Study Guide

Key Definition

The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. In geometry, both degrees and radians can be used to represent the measure of an angle. $360^\circ = 2\pi \text{ radians}$ and $180^\circ = \pi \text{ radians}$.

Important Notes

To convert degrees to radians, multiply by $\frac{\pi}{180^\circ}$.
$\pi \approx 3.14$
A full revolution in degrees is $360^\circ$.
A full revolution in radians is $2\pi$.
Radians are a dimensionless unit.

Mathematical Notation

$\times$ represents multiplication

$\pi$ is the mathematical constant Pi

$\frac{a}{b}$ represents a fraction

Remember to use proper notation when solving problems

Why It Works

Converting degrees to radians involves multiplying by $\frac{\pi}{180^\circ}$ because $180^\circ = \pi \text{ radians}$.

Remember

To convert degrees to radians, multiply by $\frac{\pi}{180^\circ}$.

Quick Reference

Convert 90° to Radians:$\frac{\pi}{2}$ or 1.571

Convert 60° to Radians:$\frac{\pi}{3}$ or 1.047

Understanding Degree to Radian Measure

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Angles in degrees divide a full rotation into 360 equal parts. To convert degrees to radians, multiply by π/180 because 180° equals π radians. For example, 90° × π/180 = π/2.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Convert $45^\circ$ to radians.

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you're designing a wheel that needs to rotate exactly $180^\circ$. How many radians is this?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What is the radian measure of a $270^\circ$ angle?

Challenge Quiz

Single Choice Quiz

Advanced

Convert $210^\circ$ to radians.

Recap

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Review key concepts and takeaways