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Radians to Degrees

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 14 of 55.

Going back is quicker. $\pi$ radians is 180°, so wherever $\pi$ appears, put 180° in its place.

Take $\frac{5\pi}{4}$ . Replace π: $\frac{5\cdot 180^{\circ}}{4}$ . A quarter of 180° is 45°, and five quarters is 225°. So $\frac{5\pi}{4}$ is 225°.

This is the same as multiplying by $\frac{180^{\circ}}{\pi}$ : the π cancels and 180° is left. Keep the degree sign in the answer. Without it the number 225 means 225 radians, about 36 full turns.

Challenge

Turn $\frac{11\pi}{6}$ into degrees. On the blank board, write x as the conversion, then a line with x worked out, keeping the ° sign. Then press Check.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Angles and the Unit Circle

1A Point on a Circle

Height on the Circle Across: the Cosine Same Height, Two Angles Recap: Height and Across

4Radians

What a Radian Is Degrees to RadiansRadians to DegreesRadians Without π Turns in Radians Recap: Radians

7Reference Angles and Signs

Reference Angles Reference in III and IV Signs by Quadrant Sign and Size Signs at Any Angle Recap: Reference Angles

10Six Functions, Any Circle

Any Circle, Any Radius From a Point to the Angle Secant, Cosecant, Cotangent Reciprocals in Radians Recap: Six Functions

2Standard Position

Angles in Standard Position Negative Angles Recap: Placing Angles

5Arc Length and Sector Area

Arc Length Arcs From Degrees Finding the Angle Sector Area Recap: A Slice of Pizza

8All Four Quadrants

Points in Quadrant II Quadrants III and IV Every Angle for a Value Points in Radians Exact Values in Radians Recap: Four Quadrants

11Final Challenges

The Minute Hand The Ferris Wheel Seat Four Angles, Two Turns The Garden Sprinkler A Negative Radian Point Which Angle?

3Coterminal Angles

Coterminal Angles Values Repeat Every Turn Every Turn at Once Recap: Coterminal Angles

6The Unit Circle

Why (cos θ, sin θ)The 30° and 60° Points The 45° Point Points Off the Table Recap: Quadrant I Points

9Tangent on the Circle

Tangent Is y over x Where Tangent Is Undefined Tangent in Radians Every Angle for a Tangent Recap: Tangent