3.12.1 Trigonometric Graphs | CIE IGCSE Maths: Extended Revision Notes 2023

Drawing Trig Graphs

Trigonometric graphs (trig graphs) are used in various applications of mathematics
- for example, the oscillating nature can be used to model how a pendulum swings or tide heights

As with other graphs, being familiar with the general style of trigonometric graphs will help you sketch them quickly and you can then use them to find values or angles alongside, or instead of, your calculator
All trigonometric graphs follow a pattern – a “starting point” and then “something happens every 90°”

y-equals-sinx

y-equals-cosx

$y = \tan x$
Starts at (0, 0)
Every 90° it is either 0 or an asymptote
- An asymptote is a line that a graph gets ever closer to, without ever crossing or touching it

y-equals-tanx

On the axes provided, sketch the graph of $y = \sin x °$ for $0 \leq x \leq 360$ .

Mark key values on the axes provided; 1, 0 and −1 on the y-axis and 0, 90, 180, 270 and 360 on the x-axis. Try to space them evenly apart

IcJiYEqM_2-14-trig-graphs1

For $y = \sin x °$ , the key knowledge is that it starts at (0, 0) then every 90° it cycles though 1, 0 , −1, 0, ... so mark these points on the axes

Finally, join the points with a smooth line. It is best practice to label the curve with its equation

5_-KJTZ8_2-14-trig-graphs2