Name:
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Topic
Algebra 
Lesson Content
 Algebraic Fractions
 Algebraic Division
Preparation Videos
 Algebraic Fractions
 Algebraic Division
Page
3
4
Consolidating Algebra
Sketching and using reciprocal trig functions
Derive Pythagorean Identities
Use Pythagorean Identities
Chain rule

C3 Reciprocal Trig Functions
5-7
Pythagorean Identities
Differentiation: Chain Rule








What is differentiation
Differentiating using the Chain Rule
Pythagorean Identities (for consolidation)
10
11
8-9
4
Differentiation: Product Rule
Differentiation: Quotient Rule


Using the product and quotient rule
Linking the product and quotient rule


Differentiating using the Product Rule
Differentiation using the quotient rule
12
13
5
Differentiating Trig functions


Differentiation consolidation
Finding the derivatives of trig functions


14
14
6
Compound Angle Formula

Use the compound angle formula

Differentiating trig function
Derivation of the derivative of sin x =cos x
(optional)
Compound angle & proof
7
Double Angle Formula
Half 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
8
Factor Formula
Consolidation

Use Double/Half angle formula to derive Factor
formula
Use the factor formula
2
Reciprocal Trig Functions
Pythagorean Identities?
3

9
A2 Transfer Challenge
GH (Purple) group only.
Visit the website now! http://mathsroots.weebly.com
2
15-16
17-20
Success in A2 = checking! The best calculator (I think) is
the Casio fx-991ES PLUS. It’s amazing because of this
button:
3
Algebraic Fractions
Before you watch anything In each of the questions below, think about what methods you
are using to reach an answer. Write them below
Simplify
12
Simplify
18
1
3
+8
3
1
2
×7
3
Simplify
Simplify
1
2
÷5
3
Key examples
Simplify
3𝑥+9
𝑥 2 +5𝑥+6
Simplify
2
5
1
+2
𝑥
𝑥+3
Simplify𝑥+2 ×
Simplify 𝑥+2 +
6𝑥+3
3
𝑥 2 +5𝑥+6
𝑥 2 +5𝑥+6
2(𝑥+3)
Simplify𝑥 2 +5𝑥+6 ÷
𝑥+3
𝑥+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)
𝑥 2 +𝑥−2
𝑥 2 −1
2)
2𝑥
𝑥+3
+
2
2𝑥+6
3)
𝑥 2 −4
𝑥−2
×
3𝑥
2𝑥−4
Having problems with this topic? Watch these videos:
4
4)
14
𝑥+2
÷
7
𝑥 2 −𝑥−6
Algebraic Division
Before you 3𝑥 + 3
1
watch
2−1
𝑥
anything:
Simplify the
fraction opposite.
What do you
notice about
what you’re left
with?
7
3
𝑥 3 + 𝑥 2 + 2𝑥 − 1
𝑥2 − 1
Don’t forget to do your checks!
Substitute x=0.1 into the question and your answer and check
you get the same value
5
We’ll sketch
these
functions in
class!
Reciprocal Trig Functions
Reciprocal means....
1
sin 𝑥
𝑥
1
cos 𝑥
0 ≤ 𝑥 < 90
90 ≤ 𝑥 < 180
1
tan 𝑥
At 𝑥 = 180
sin 𝑥
1
sin 𝑥
6
180 < 𝑥 ≤ 270
270 < 𝑥 ≤ 360
𝑥
0 ≤ 𝑥 < 90
At 𝑥 = 90
At 𝑥 = 0
0 < 𝑥 ≤ 90
180 < 𝑥 < 270
90 < 𝑥 ≤ 180
At 𝑥 = 270
270 < 𝑥 ≤ 360
cos 𝑥
1
cos 𝑥
𝑥
At 𝑥 = 180
90 < 𝑥 < 180
tan 𝑥
1
tan 𝑥
7
180 < 𝑥 ≤ 270
270 < 𝑥 ≤ 360
Solving reciprocal trig functions
𝑐𝑜𝑠𝑒𝑐 1.8 =
𝑐𝑜𝑡 0.7 =
3𝜋
𝑐𝑜𝑡
=
11
Solve for 0 ≤ 𝑥 ≤ 180
sec 𝑥 = 3
cot 𝑥 = 0.1
8
More Pythagorean Identities
𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 ≡ 1
What happens if I move the 1?
Another way of deriving them...
9
To be able to do the next part of trig we need some new
differentiation techniques....
Key Examples
(sec 𝑥 − sin 𝑥)(sec 𝑥 + sin 𝑥) ≡ 𝑡𝑎𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥
𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 360,
𝑠𝑒𝑐 2 𝑥 = 3 tan 𝑥
10
We’ll go
through
these in
class!
Differentiation: what is it anyway?
11
Differentiation: the chain rule
𝑦 = (3𝑥 2 + 6𝑥)7
Where has this come from?
12
We’ll go
through
these in
class!
Differentiation: the product rule
𝑦 = 𝑥 4 sin 𝑥
Where has this come from?
13
We’ll go
through
these in
class!
Differentiation: the quotient rule
sin 𝑥
𝑦=
3𝑥 7
Where has this come from?
14
We’ll go
through
these in
class!
Differentiating Trig functions
Derivatives 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 2𝐴
cos 2𝐴
Half angle formula
18
Double/Half Angle Formula: Key
examples
19
We’ll
complete
this in class!
Factor Formula
𝐴+𝐵
𝐴−𝐵
sin 𝐴 + sin 𝐵 = 2 sin (
) cos (
)
2
2
Use a formula book (or google edexcel formula book) to find the other 3
factor formulae...
20
21
Factor Formula: Key example
22