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Year 9 Trigonometry

Year 9 Trigonometry. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 5 th October 2013. Starter. Frost Childhood Story. y. ( a,b ). I was trying to write a program that would draw an analogue clock.

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Year 9 Trigonometry

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  1. Year 9 Trigonometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5th October 2013

  2. Starter Frost Childhood Story y (a,b) 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. θ r x

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

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

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

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

  7. Sin/Cos/Tan sin, cos and tan give us the ratio between pairs of sides in a right angle triangle, given the angle. ? h o ? θ a ? “sohcahtoa”

  8. Example 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: opposite tan(45) = 1 ? ? 45 adjacent

  9. More Examples Step 1: Determine which sides are hyp/adj/opp. Step 2: Work out which trigonometric function we need. Find (to 3sf) 7 4 x 20 ° 40 ° x ? ?

  10. More Examples ? x x 60 ° 4 30° 12 ?

  11. Exercises 1 Find , giving your answers to . Please copy the diagrams first. ? ? c b a ? 22 f e d 15 ? 4 ? ? 20 10 2 I put a ladder 1.5m away from a tree. The ladder is inclined at above the horizontal. What is the height of the tree? Ship B is 100m east of Ship A, and the bearing of Ship B from Ship A is . How far North is the ship? Find . ? 3 ? ? 4

  12. Frost Childhood Story y θ x So what is ?

  13. Recap: Find x ? 4 30 ° x

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

  15. What is the missing angle?

  16. What is the missing angle?

  17. What is the missing angle?

  18. What is the missing angle?

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

  20. Real-World Example 3.19m 60° 40° x 3m Find x

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

  22. Level 2 – Q3

  23. Level 3 – Q1

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