Year 9 Trigonometry Dr J Frost Last modified: 2 nd November 2014

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 HypotenuseOppositeAdjacent xyz √211 cab 45° 1 √2 1 20° a c b ??? ??? ??? Names of sides relative to an angle

“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 ? ? ?

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 ? ??

40 ° 4 20 ° 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 a b c d e f 2 3 11 ? ? ? ? ? ? ? ? 22 ? ?

x y θ

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?

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

Exercise 2 ? ? ? ? ? ? ? 1 

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