Menu

The Midline

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 19 of 49.

Add a number outside the sine and every height goes up by it. $y = \sin\left(x\right)+2$ is the sine wave lifted 2: it now swings between 1 and 3, around the line y = 2.

$y = sin x + 2 swinging between 1 and 3 around the dashed line y = 2$

That line is the midline. For $y = a\cdot \sin\left(x\right)+k$ with a positive, the midline is y = k, the top is k + a and the bottom is k − a. The wave crosses its midline where the plain sine crosses the x axis.

A negative k moves the wave down: $y = \sin\left(x\right)-3$ swings between −4 and −2.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y = 2\cos x-1

Draw the wave

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs of Trig Functions

2The Cosine Graph

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

5Midline

The MidlineFrom 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