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Where Sine Meets Cosine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 7 of 49.

$The sine and cosine waves over one lap, crossing twice$

In one turn the two waves cross twice. Where they cross, the point's height equals its across. So the point is on the line y = x. That happens at 45°, and at the opposite point, 225°, where both are −√2/2. These are the angles where $\tan\left(x\right) = 1$ .

Challenge

Find every angle from 0 up to 4π where the sine and cosine waves cross. That is where $\tan\left(\theta\right) = 1$ . Tap them on the circle.

Then press Check.

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

All lessons in Graphs of Trig Functions

2The Cosine Graph

The Cosine Graph Cosine Is a Shifted SineWhere Sine Meets CosineCosine 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