Trigonometric Graphs (AQA GCSE Maths: Higher): Revision Note

Drawing trig graphs

What are trig graphs?

• Trigonometric (trig) graphs are the graphs of

  • $y=\sin x$

  • $y=\cos x$

  • $y=\tan x$

• The variable $x$ is like an angle

  • but the angle can now go beyond acute to become obtuse and reflex

    • $0°\le x\le 360°$

• Trig graphs have repeating (periodic) shapes and symmetries that you need to know

What is the shape of the graph of y = sin x?

• The graph of $y=\sin x$ is a wave that oscillates between heights of 1 and -1 and repeats every 360° (its period is 360°)

  • It goes through the origin, (0, 0)

  • Plot a point whenever $x$ is a multiple of 90°

    • The $y$ coordinates cycle through the numbers 0, 1, 0, -1

What is the shape of the graph of y = cos x?

• The graph of $y=\cos x$ is a wave that oscillates between heights of 1 and -1 and repeats every 360° (its period is 360°)

  • It has a y-intercept of 1, coordinates (0, 1)

  • Plot a point whenever $x$ is a multiple of 90°

    • The $y$ coordinates cycle through the numbers 1, 0, -1, 0

• $y=\cos x$ is the same as translating $y=\sin x$ by 90 to the left

What is the shape of the graph of y = tan x?

• The graph of $y=\tan x$ is not a wave but consists of branches that repeat every 180° (its period is 180°)

  • This is half the period of $\sin x$ and $\cos x$

• There are dotted vertical lines that separate the branches called asymptotes

  • These are every 180° at $x=90°$, $x=270°$, ...

  • The curve cannot touch these, but get closer and closer to them

  • A branch starts down at a height of $-\infty$ and goes up to a height of $+\infty$

• $y=\tan x$ goes through the origin, (0, 0)