1. Year 9 Trigonometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd November 2014

2. x y θ (a,b) r I was trying to write a program that would draw an analogue clock. I needed to work out between what two points to draw the hour hand given the current hour, and the length of the hand. Starter

3. 3 4 x 13 5 y Question: What do we require for the theorem to work? What you already know

4. 30° 4 x y What is x and what is y? What you’re less likely to know...

5. 30° hypotenuse adjacent opposite Names of sides relative to an angle ? ? ?

6. 60° x y z HypotenuseOppositeAdjacent xyz √211 cab 45° 1 √2 1 20° a c b ??? ??? ??? Names of sides relative to an angle

7. “soh cah toa”  sin, cos and tan are functions which take an angle and give us the ratio between pairs of sides in a right angle triangle. Sin/Cos/Tan ? ? ?

8. Example 45 opposite adjacent Looking at this triangle, how many times bigger is the ‘opposite’ than the ‘adjacent’ (i.e. the ratio) Ratio is 1 (they’re the same length!) Therefore: tan(45) = 1 ? ??

9. 40 ° 4 20 ° 7 Step 1: Determine which sides are hyp/adj/opp. Step 2: Work out which trigonometric function we need. More Examples ? ?

10. 60 ° 12 30° 4 More Examples ? ?

11. Exercise 1 15 1 22 a b 20 10 4 c d e f 2 3 11 ? ? ? ? ? ? ? ? 22 ? ?

12. x y θ

13. 30 ° 4 RECAP: Find x ?

14. 3 5 But what if the angle is unknown? ? ? We can do the ‘reverse’ of sin, cos or tan to find the missing angle.

15. What is the missing angle?

19. 2 3 θ 1 3 “To learn secret way of math ninja, find θ you must.” 1 1 θ 6 θ 8 1 2 3 4 θ ? ? ? ?

20. Exercise 2 ? ? ? ? ? ? ? 1  2 3 4 5 6

21. x 40 ° 60 ° 3m Find x 3.19m

22. Trig Challenge Stage 1 The kind of problems that you’re likely to find in a landmark exam. Stage 2 Stage 3 Problems you might find as a harder landmark question or in a GCSE exam. More difficult problems that will help you become adept mathematicians.

23. Level 2 – Q3

24. Level 3 – Q1