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Same Height, Two Angles

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 3 of 55.

$P at 30° and Q at 150°, mirror images across the y-axis at the same height$

P is at 30° and Q is at 150°. Fold the picture along the y-axis and P lands on Q. So they are at the same height: $\sin\left(30^{\circ}\right)$ and $\sin\left(150^{\circ}\right)$ are both 1/2.

Folding along the y-axis keeps the height and changes the sign of the across. So θ and 180° − θ have the same sine.
Folding along the x-axis keeps the across and changes the sign of the height. So θ and −θ have the same cosine.

With these two folds you can find every angle with a given height.

Challenge

Tap every angle in one turn where the height is minus one half. That is where $\sin\left(\theta\right) = \frac{-1}{2}$ .

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 CosineSame Height, Two AnglesRecap: 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 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