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Back Into One Turn

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 10 of 57.

Every angle has exactly one coterminal angle from 0° up to (not including) 360°. To find it, add or subtract whole turns.

For 1000°, subtract: 1000 − 360 is 640, still more than a turn, so subtract again. Two turns at once is 720°, and 1000° - 720° = 280°. For a negative angle, add turns until it is positive: -200° + 360° = 160°.

On the board, write the angle with the turns added or taken away, then work it out. A quick check: the answer must land between 0° and 360°. If it does not, you used too few turns or too many.

Challenge

Find the angle x from 0° up to 360° that is coterminal with -500°. On the blank board, write x as −500° with whole turns added, then a line with x worked out (keep 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 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 Quadrants and Axes 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 AnglesBack Into One TurnValues 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