Graphs of Trigonometric Functions
What is meant by graphs of trigonometric functions?
- The graphs are
Why do I need to know what graphs of trigonometric functions look like?
- Trigonometric graphs (trig graphs) are used in various applications of mathematics
- e.g. the oscillating / wave-like nature of sine and/or cosine can be used to model how a pendulum swings or tide heights
How do I sketch trig graphs?
- As with other graphs, being familiar with the general style of trig graphs will help you sketch them quickly
- They can then be used to find values or angles alongside, or instead of, your calculator
- All trig graphs follow a pattern – a “starting point” and then “something happens every 90°”
- The diagrams below show the graphs of sin, cos and tan from -360° to 360°
- Most questions will focus on the postive part of the graph for angles between 0° and 360°
Worked example
On the axes provided, sketch the graph of for .
Mark key values on the axes provided; 1and −1 on the y-axis and 90, 180, 270 and 360 on the x-axis
Try to space them evenly apart but also remember this is a sketch!
starts at (0, 0) then every 90° it cycles though 1, 0 , −1, 0, ...
Mark these points on the axes
Finally, join the points with a smooth curve
You will get better at this with practice but again remember it is a sketch so do not spend ages making it look perfect!
It is best practice to label the curve with its equation