Name: …………………………………

1

Topic Lesson Content Preparation Videos Page1 Algebra Algebraic Fractions

Algebraic Division Algebraic Fractions Algebraic Division

34

2 Reciprocal Trig FunctionsPythagorean Identities?

Consolidating Algebra Sketching and using reciprocal trig functions Derive Pythagorean Identities

C3 Reciprocal Trig Functions 5-7

3 Pythagorean IdentitiesDifferentiation: Chain Rule

Use Pythagorean Identities Chain rule

What is differentiation Differentiating using the Chain Rule Pythagorean Identities (for consolidation)

10118-9

4 Differentiation: Product RuleDifferentiation: Quotient Rule

Using the product and quotient rule Linking the product and quotient rule

Differentiating using the Product Rule Differentiation using the quotient rule

1213

5 Differentiating Trig functions Differentiation consolidation Finding the derivatives of trig functions

Differentiating trig function Derivation of the derivative of sin x =cos x

(optional)

1414

6 Compound Angle Formula Use the compound angle formula Compound angle & proof 15-16

7 Double Angle FormulaHalf Angle Formula

Derive and use the double angle formula Derive and use the half angle formula

Double half factor formulae Core 3 – Trigonometry – Solomon Paper D – Q2

17-20

8 Factor FormulaConsolidation

Use Double/Half angle formula to derive Factor formula

Use the factor formula

9 A2 Transfer Challenge GH (Purple) group only.

Visit the website now! http://mathsroots.weebly.com Success in A2 = checking! The best calculator (I think) is

2

the Casio fx-991ES PLUS. It’s amazing because of this button:

3

Algebraic FractionsBefore you watch anything In each of the questions below, think about what methods you are using to reach an answer. Write them belowSimplify 1218 Simplify 13+

38 Simplify 13×

27 Simplify 13 ÷

25

Key examplesSimplify 3 x+9x2+5 x+6

Simplify 6 x+31x+2

Simplify 5x+2

+ 3x2+5 x+6

Simplify2x+2

× x2+5 x+62( x+3)

Simplifyx+3

x2+5 x+6÷ x+3x+2

Don’t forget to do your checks!Substitute x=0.1 into the question and your answer and check you get the same value

4 quick questions: Simplify,..

1) x2+x−2x2−1

2) 2 xx+3 + 22x+6 3) x

2−4x−2

× 3 x2x−4 4) 14x+2 ÷

7x2−x−6

4

Having problems with this topic? Watch these videos:

Algebraic Division Before you watch anything: Simplify the fraction opposite. What do you notice about what you’re left with?

3 x+31x2

−1

73

x3+x2+2 x−1x2−1

5

Don’t forget to do your checks!Substitute x=0.1 into the question and your answer and check you get the same value

Reciprocal Trig FunctionsReciprocal means....

1sin x

1cos x

1tan x

x 0≤ x<90 90≤ x<180 At x=180 180<x ≤270 270<x ≤360

sin x

1sin x

6

We’ll sketch these functions in class!

x 0≤ x<90 At x=90 90<x ≤180 180<x<270 At x=270 270<x ≤360

cos x

1cos x

x At x=0 0<x ≤90 90<x<180 At x=180 180<x ≤270 270<x ≤360

tan x

1tan x

7

Solving reciprocal trig functions cosec 1.8=¿

cot 0.7=¿

cot 3π11

=¿

Solve for 0≤ x≤180sec x=3 cot x=0.1

8

More Pythagorean Identitiessin2 x+cos2 x≡1

What happens if I move the 1?

Another way of deriving them...

To be able to do the next part of trig we need some new differentiation techniques....

9

Key Examples ¿

Solve for0≤ x≤360 ,sec2 x=3 tan x

10

We’ll go through these

in class!

Differentiation: what is it anyway?

11

Differentiation: the chain rule

y=(3 x2+6 x )7

Where has this come from?

12

We’ll go through these

in class!

Differentiation: the product rule

y=x4 sin x

Where has this come from?

13

We’ll go through these

in class!

Differentiation: the quotient rule

y= sin x3 x7

Where has this come from?

14

We’ll go through these

in class!

Differentiating Trig functionsDerivatives of sin x and cos x (optional: watch the proof. You’ll need to watch the compound angle formula video first – see C3 Trigonometry)

The remaining 4 derivatives...

15

Compound Angle Formula

16

Compound Angle Formula: Key Examples

17

We’ll complete this in class!

Double Angle Formula sin 2 A

cos2 A

Half angle formula

18

Double/Half Angle Formula: Key examples

19

We’ll complete this in class!

Factor Formulasin A+sin B=2sin( A+B

2 )cos ( A−B2 )

Use a formula book (or google edexcel formula book) to find the other 3 factor formulae...

20

Factor Formula: Key example

21