A Negative a Flips It

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 11 of 49.

In $y = -2\sin\left(x\right)$ 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: $y = -\cos\left(x\right)$ 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 = -3\cos x

Draw the wave

Test yourself

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

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8The Tangent Graph

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3Amplitude

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6Phase Shift

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9Modelling with Waves

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