Graphs of sine and cosine

Plotting on a Cartesian plane the value of $\sin\alpha$ and $\cos\alpha$ as $\alpha$ varies, one obtains two wavy curves, the sinusoids.

The graphs of $\sin x$ and $\cos x$ between $-2\pi$ and $2\pi$. Both oscillate between $-1$ and $+1$, with period $2\pi$.

The graph of $\cos$ is the graph of $\sin$ translated by $\pi/2$ to the left: $\cos\alpha = \sin(\alpha+\pi/2)$. The $\sin$ is odd ($\sin(-\alpha)=-\sin\alpha$, graph symmetric about the origin), the $\cos$ is even ($\cos(-\alpha)=\cos\alpha$, symmetric about the $y$ axis).

In the simulation below you can explore how the parameters $A$, $B$, $C$, $D$ transform the sinusoid $y=A\sin(Bx+C)+D$.

Drag the sliders: $y=A\sin(Bx+C)+D$ — amplitude $A$, angular frequency $B$, phase $C$, vertical shift $D$.

Links

Topics: Trigonometry
Concepts: Cosine · Odd function · Even function · Periodicity · Sine
Functions: Cosine · Sine
Skills: Interpreting a graph · Drawing a graph