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The 30° and 60° Points

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 26 of 57.

Half an equilateral triangle is a 30-60-90 triangle. With hypotenuse 1, the side opposite 30° is half of it, 1/2, and Pythagoras gives the other leg: √(1 - 1/4) = √(3)/2.

$The point at 30° on the unit circle, (√3/2, 1/2)$

At 30° the long leg is the across and the short leg the height, so the point is (√(3)/2, 1/2): cos(30°) = √(3)/2 and sin(30°) = 1/2.

Stand the same triangle on its other end and the 60° angle is at the centre. Which leg is which is then the whole question: the leg opposite the angle at the centre is the height.

Challenge

Set the coordinates of the point at 60°, 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 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° PointsThe 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