Negative Angles

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 6 of 55.

Two clockwise quarter turns make $-180^{\circ}$ . Clockwise turns are negative. A turn of 60° clockwise ends where a turn of 300° counterclockwise ends. So $-60^{\circ}$ ends where 300° ends. In general, −θ ends where 360° − θ ends.

$An angle of −150°: a clockwise turn ending in quadrant III$

Challenge

Tap every angle from −360° up to 0° where the across is 0. That is where $\cos\left(\theta\right) = 0$ .

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 PositionNegative AnglesRecap: 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