Trigonometric Graphs (Edexcel GCSE Maths): Revision Note

Drawing Trig Graphs

What are trig graphs?

• Trigonometric (trig) graphs are the graphs of

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• The variable is like an angle

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

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

How do I draw the graph of y = sin x?

• The graph of 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)

  • Then every 90° it cycles through the heights 1, 0, -1, 0, ...

How do I draw the graph of y = cos x?

• The graph of 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)

  • Then every 90° it cycles through the heights 0, -1, 0, 1, ...

• is the same as translating by 90 to the left

How do I draw the graph of y = tan x?

• The graph of is not a wave but consists of branches that repeat every 180° (its period is 180°)

  • This is half the period of and

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

  • These are every 180° at , , ...

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

  • A branch starts down at a height of and goes up to a height of

• goes through the origin, (0, 0)