IGCSE FM Trigonometry Dr J Frost Last modified: 18 th April 2016 Objectives: (from the specification)

Sin Graph What does it look like? ?

Sin Graph What do the following graphs look like? 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 ???

Cos Graph What do the following graphs look like? ?

Cos Graph What does it look like? 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 ? ? ?

Tan Graph What does it look like? ?

Tan Graph What does it look like? 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 ??

Solving Trig Equations ? 0.6 ?

Solving Trig Equations ? ? ?

Solving Trig Equations ? -0.3 ?

Laws of Trigonometric Functions ? ? ? ? 

Set 4 Paper 2 Q14 Test Your Understanding ? ? ?

Exercise a b c d e f g a b c d e f ? ? ? ? ? ? ? ? ? ? ? ? ?

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. ?

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.

Test Your Understanding ? ?

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

More Examples ? ?

Test Your Understanding ? ?

Exercise ? ? ? ? ? ? ? ? ? ? ? 3 4  a b a b c a b c a b

Review of what we’ve done so far partly

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

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

Test Your Understanding AQA Worksheet ? ?

Exercise 3 ? ? ? ? 1 2 3

? 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. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Example Exam Questions ? Mark Scheme

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