Trigonometric Graphs (Cambridge International IGCSE Mathematics)

Drawing Trig Graphs

What are trig graphs?

• Trigonometric (trig) graphs are the graphs of

  • $y=\mathrm{sin}x$
  • $y=\mathrm{cos}x$
  • $y=\mathrm{tan}x$

• The variable $x$ is like an angle

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

    • $0^{\circ}\leq x\leq360^{\circ}$

• 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 $y=\mathrm{sin}x$ 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 $y=\mathrm{cos}x$ 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

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

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

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

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

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

  • These are every 180° at $x=90^{\circ}$, $x=270^{\circ}$, ...
  • 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 $+\infty$

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