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Quadrants III and IV

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 35 of 55.

Below the x-axis the height is negative. In quadrant III the across is negative too; in quadrant IV it is positive.

$The point at 240° on the unit circle, (−1/2, −√3/2)$

240° is in quadrant III with reference angle 60°: sizes 1/2 across and √3/2 up, both made negative, so the point is ( $\frac{-1}{2}$ , $\frac{-\sqrt{3}}{2}$ ). 330° is in quadrant IV with reference angle 30°: across √3/2 stays positive, the height 1/2 turns negative, ( $\frac{\sqrt{3}}{2}$ , $\frac{-1}{2}$ ).

The method never changes: reference angle for the sizes, quadrant for the signs.

Challenge

Set the coordinates of the point at $315^{\circ}$ , 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 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 IIQuadrants III and IVEvery 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