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Quadrants and Axes

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 7 of 57.

The axes cut the plane into four quadrants, numbered counterclockwise: I upper right, II upper left, III lower left, IV lower right. For an angle from 0° to 360° the quadrant comes from where it sits between the axes: I between 0° and 90°, II between 90° and 180°, III between 180° and 270°, IV between 270° and 360°.

$The four quadrants, numbered I to IV counterclockwise from the upper right$

An angle that ends exactly on an axis, such as 90° or 180°, is a quadrantal angle and belongs to no quadrant. That matters later: the quadrant decides the signs of sine and cosine, and on an axis one of them is 0, which has no sign.

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 AnglesQuadrants and AxesRecap: 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 Back Into One Turn 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