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

The Graph of tan  "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Module C2

The Graph of tan  We are going to sketch the graph of where is an angle between and.

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

The Graph of tan  x The graphs of and for are

The Graph of tan  y x The graphs of and for are x

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

The Graph of tan  x The graphs of and for are x x x x x x

The Graph of tan  x The graphs of and for are x x x x xx x x xx

The Graph of tan  x The graphs of and for are x x x x xx x x xx

The Graph of tan  The graph of repeats every...

The Graph of tan  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.

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

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

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

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

The Graph of tan 

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

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