Year 9 Trigonometry Dr J Frost jfrosttiffinkingstonschuk Last modified 2 nd November 2014 Frost Childhood Story x y θ ab r I was trying to write a program that would draw an analogue clock ID: 763704
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Year 9 Trigonometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd November 2014
Frost Childhood Story 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 4 x 13 5 y Question: What do we require for the theorem to work? What you already know
30° 4 x y What is x and what is y? What you’re less likely to know...
30° hypotenuse adjacent opposite Names of sides relative to an angle ? ? ?
60° x y z Hypotenuse Opposite Adjacent x y z √2 1 1 c a b 45° 1 √2 120° a c b ? ? ? ? ? ? ? ? ? Names of sides relative to an angle
“ s oh c ah t oa ” ! 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 ? ? ?
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 ? ? ?
4 0 ° 4 Find (to 3sf) 2 0 ° 7 Step 1: Determine which sides are hyp / adj /opp. Step 2: Work out which trigonometric function we need. More Examples ? ?
60 ° 12 30° 4 More Examples ? ?
Exercise 1 Find , giving your answers to . Please copy the diagrams first. 15 1 22 a b 20 10 4 c d e f 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 the exact value of . 2 3 N 1 ? ? ? ? ? ? ? ? [IMC] The semicircle and isosceles triangle have equal areas. Find . N 2 ? ?
Frost Childhood Story x y θ So what is ?
30 ° 4 RECAP : Find x ?
3 5 But what if the angle is unknown? ? ? We can do the ‘reverse’ of sin, cos or tan to find the missing angle.
What is the missing angle?
What is the missing angle?
What is the missing angle?
What is the missing angle?
The Wall of Trig Destiny 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 ? ? ? ?
Exercise 2 Find , giving your answer to 3sf. The angles form a sequence. Give the formula for the th term of the sequence. ? ? ? ? ? ? ? 1 N 2 3 4 5 6
Real-World Example x 40 ° 60 ° 3m Find x 3.19m
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 .
Level 2 – Q3
Level 3 – Q1