Graphs of Trigonometric Functions

Starting point: Years 9 and 10

Plotting y = sin x

Use your calculator to fill a table from $0^{\circ }$ to $360^{\circ }$:

Plot and join smoothly to get two waves.

Words for waves

• The amplitude is the height from the centre line to a peak. For $y=\sin x$ it is 1.
• The period is the length of one full cycle. For $y=\sin x$ it is $360^{\circ }$.
• The centre line of $y=\sin x$ is $y=0$.

Quick summary

• $y=\sin x$ and $y=\cos x$ are waves between $-1$ and $1$ with period $360^{\circ }$, or $2\pi$.
• Cosine is sine moved left by $90^{\circ }$.
• $y=\tan x$ has period $\pi$ and asymptotes where $\cos x=0$.
• $y=a\sin (bx)$: amplitude $|a|$, period $\frac{2\pi }{b}$.
• $y=a\sin (b(x-c))+d$: $c$ shifts right, $d$ moves the centre line.

Quiz