A Negative a Flips It

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 13 of 51.

In y = -2sin(x) every height of 2 sin x changes sign. Where 2 sin x has its top, 2 at π/2, the new graph has its bottom, −2. The wave is reflected in the x axis: it falls first instead of rising.

$y = -2 sin x, the reflection of y = 2 sin x in the x axis$

The amplitude is a distance, so it is never negative: the amplitude of −2 sin x is 2. The sign of a only says which way the wave sets off.

A flipped cosine starts at its bottom: y = -cos(x) is −1 at 0 and reaches its top, 1, at π.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=-3cos(x)

Draw the graph

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

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5Midline

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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 CosineA Negative a Flips ItAmplitude 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