4. Trigonometry

c. Circle Definitions

On this page, you will get to manipulate the generic sine and cosine functions and learn the meanings of the period \(P\), the amplitude \(A\), the phase \(\phi\) and the median \(M\). (It is easier to understand the meaning of phase using the cosine function.)

5. Properties of Sine and Cosine Curves

Generic Sine Function

Below is the graph of \(y=A\sin\left(2\pi\dfrac{x}{P}-\phi\right)+M\).
Read the hints to learn the definitions of the period \(P\), the amplitude \(A\), the phase \(\phi\) and the median \(M\).
Try moving the sliders or typing in the text boxes to see what happens to the graph.

Generic Cosine Function

Below is the graph of \(y=A\cos\left(2\pi\dfrac{x}{P}-\phi\right)+M\), where the period is \(P\), the amplitude is \(A\), the phase is \(\phi\) and the median is \(M\). Try moving the sliders to see what happens to the graph.

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