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Unrolling the Sine Graph

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 2 of 49.

$The sine wave over two laps, from 0 to 720 degrees$

This is the graph of $y = \sin\left(x\right)$ . It shows the height of the point on a circle of radius 1, turn after turn. The height goes up to 1 at 90°. It is 0 again at 180°. It goes down to −1 at 270° and is 0 again at 360°. Then the next turn draws the same wave. The wave repeats every 360°. This length is called its period.

Challenge

Find every angle in the first two turns, from 0° up to 720°, where the wave is at height $\frac{-\sqrt{3}}{2}$ . Tap them on the circle. The point's height is the wave's height.

Then press Check.

Start the lesson to read it in the interactive player and track your progress.

All lessons in Graphs of Trig Functions

1From Circle to Wave

Ride a Ferris WheelUnrolling the Sine GraphThe Sine Graph in Radians Circle to Wave Recap

4Period

Period: One Wave Long Stretching the Wave Period in Degrees b Is Not the Period Period Recap

7Reading a Graph

The Equation of a Wave Sine or Cosine?From Peaks to a Wave All Four at Once Reading Recap

10Final Challenges

A Wave From Its Facts A Hidden Shift A Flipped Tangent Read the Whole Wave Giant Wheel: the Model Giant Wheel: the Height

2The Cosine Graph

The Cosine Graph Cosine Is a Shifted Sine Where Sine Meets Cosine Cosine Graph Recap

5Midline

The Midline From Highest and Lowest Reading the Midline Midline Recap

8The Tangent Graph

The Tangent Graph Asymptotes Stretching the Tangent Graphs of sec, csc and cot Tangent Recap

3Amplitude

Amplitude: How Tall Amplitude of a Cosine A Negative a Flips It Amplitude From a Graph Amplitude Recap

6Phase Shift

Phase Shift: Sliding Phase Shift in Degrees Factor Out b First Reading a Phase Shift Phase Shift Recap

9Modelling with Waves

A Ferris Wheel Model Daylight Over a Year Tides Using a Model A Spring's Bounce Modelling Recap