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Every Turn at Once

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 10 of 55.

In one turn the height is 1/2 at 30° and 150°. Spin the point for two turns: how many times does it pass that height?

After every full turn, the point is back where it was. So find the angles in the first turn. Then add 360° to each one, again and again, until you pass the end of the interval. For example, the bottom of the circle, where $\sin\left(\theta\right) = -1$ , comes once a turn: at 270°, 630° and 990°.

Challenge

Tap every angle from 0° up to 720° where the across is one half. That is where $\cos\left(\theta\right) = \frac{1}{2}$ . This is two turns, so look at both.

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 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 TurnEvery Turn at OnceRecap: 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