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

2. 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

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

4. 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

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

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

7. 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.

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

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

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

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

12. 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.

13. 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

14. 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

15. 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

16. 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

17. The Graph of tan 

18. 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.

19. 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

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