1. IGCSE FM Trigonometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 18 th April 2016 Objectives: (from the specification)

2. Sin Graph What does it look like? 90180270360 -90-180-270-360 ?

3. Sin Graph What do the following graphs look like? 90180270360 -90-180-270-360 Suppose we know that sin(30) = 0.5. By thinking about symmetry in the graph, how could we work out: sin(150) = 0.5sin(-30) = -0.5sin(210) = -0.5 ???

4. Cos Graph What do the following graphs look like? 90180270360 -90-180-270-360 ?

5. Cos Graph What does it look like? 90180270360 -90-180-270-360 Suppose we know that cos(60) = 0.5. By thinking about symmetry in the graph, how could we work out: cos(120) = -0.5cos(-60) = 0.5cos(240) = -0.5 ? ? ?

6. Tan Graph What does it look like? 90180270360 -90-180-270-360 ?

7. Tan Graph What does it look like? 90180270360 -90-180-270-360 Suppose we know that tan(30) = 1/ √ 3. By thinking about symmetry in the graph, how could we work out: tan(-30) = -1/√3tan(150) = -1/√3 ??

8. Solving Trig Equations 90180270360 -90-180-270-360 ? 0.6 ?

9. Solving Trig Equations 90180270360 -90-180-270-360 ? ? ?

10. Solving Trig Equations 90180270360 -90-180-270-360 ? -0.3 ?

11. Laws of Trigonometric Functions ? ? ? ? 

12. Set 4 Paper 2 Q14 Test Your Understanding ? ? ?

13. Exercise 1 1 2 a b c d e f g a b c d e f ? ? ? ? ? ? ? ? ? ? ? ? ?

14. Trigonometric Identities 1  1 2 Pythagoras gives you... ? ? ? Using basic trigonometry to find these two missing sides… These two identities are all you will need for IGCSE FM. ?

15. Application #1: Solving Harder Trig Equations The problem here is that we have two different trig functions. Is there anything we could divide by to get just one trig function? ? ? ? Bro Tip: In general, when you have a mixture of sin and cos, divide everything by cos.

16. Test Your Understanding ? ?

17. Application #1: Solving Harder Trig Equations This looks a bit like a quadratic. What would be our usual strategy to solve! ? ? ? June 2013 Paper 2 Q22

18. More Examples ? ?

19. Test Your Understanding ? ?

20. Exercise 2 1 2 ? ? ? ? ? ? ? ? ? ? ? 3 4  a b a b c a b c a b

21. Review of what we’ve done so far partly

22. Application of identities #2: Proofs We want to use these… ? ? ? ?

23. Another Example June 2012 Paper 1 Q16 Bro Tip: Whenever you have a fraction in a proof question, always add the fractions. ? ? ? ?

24. Test Your Understanding AQA Worksheet ? ?

25. Exercise 3 ? ? ? ? 1 2 3

26. ? You need to be able to calculate these in non-calculator exams. All you need to remember:  Draw half a unit square and half an equilateral triangle of side 2. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

27. Example Exam Questions ? Mark Scheme

28. Using triangles to change between sin/cos/tan ? ? Represent as a triangle ? ? Test Your Understanding ? ? ? ? 12