“Teach A Level Maths” Vol. 1: AS Core Modules 38: The graph of tanq © Christine Crisp

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We are going to sketch the graph of where is an angle between and .

x y O Draw a circle, radius 1, with centre at the origin and complete a triangle. P (x, y) From the triangle, y and N Also, x So, To sketch the graph of we can divide values of and taken from their graphs.

The graphs of and for are x

The graphs of and for are y x x

The graphs of and for are This line, where is not defined is called an asymptote. x x x Dividing by zero gives infinity so is not defined when .

The graphs of and for are x x x x x x x

The graphs of and for are x x x x x x x x x x x

The graphs of and for are x x x x x x x x x x x

The graph of repeats every . . .

is defined for angles less than and greater than in the same way as the other trig functions so the graph can be extended. e.g. . . . it is cyclic with a period of .

Exercise Sketch the graph of for values of from to clearly showing the asymptotes. Use the graph to give a value of between and ( not equal to the given angle! ) where (a) (b) (c) (d) (a) Solution: x x

Exercise Sketch the graph of for values of from to clearly showing the asymptotes. Use the graph to give a value of between and ( not equal to the given angle! ) where (a) (b) (c) (d) (a) (b) x x

Exercise Sketch the graph of for values of from to clearly showing the asymptotes. Use the graph to give a value of between and ( not equal to the given angle! ) where (a) (b) (c) (d) (a) x (b) x x (c) or

Exercise Sketch the graph of for values of from to clearly showing the asymptotes. Use the graph to give a value of between and ( not equal to the given angle! ) where (a) (b) (c) (d) (a) (b) x x (c) or (c) (d)

The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

N Draw a circle, radius 1, with centre at the origin and complete a triangle. P (x, y) x y O Also, So, To sketch the graph of we can divide values of and taken from their graphs. From the triangle, and

The graph of repeats every . . . . . . it is cyclic with a period of .