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Coterminal Angles

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 8 of 55.

A skateboarder spins 540° in the air and lands facing backwards. 540° is a full turn, then 180° more. A full turn of 360° does not change where an angle ends. Angles that end in the same place are called coterminal. To bring any angle into one turn, add or subtract 360° until it is from 0° up to 360°. For example, $-200^{\circ}+360^{\circ} = 160^{\circ}$ .

Challenge

Which angle x from 0° up to 360° ends where −500° ends? Write x as −500° plus whole turns, then work it out. Keep the ° sign.

Then press Check.

Start the lesson to read it in the interactive player 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 Radians Radians to Degrees Radians 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 AnglesValues 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