Roots. · Web viewTopic Lesson Content Preparation Videos Page 1 Algebra Algebraic Fractions Algebraic Division Algebraic Fractions Algebraic Division 3 4 2 Reciprocal Trig Functions
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Topic Lesson Content Preparation Videos Page1 Algebra Algebraic Fractions
Algebraic Division Algebraic Fractions Algebraic Division
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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
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the Casio fx-991ES PLUS. It’s amazing because of this button:
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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 ÷
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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
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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
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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
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Solving reciprocal trig functions cosec 1.8=¿
cot 0.7=¿
cot 3π11
=¿
Solve for 0≤ x≤180sec x=3 cot x=0.1
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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....
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Key Examples ¿
Solve for0≤ x≤360 ,sec2 x=3 tan x
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We’ll go through these
in class!
Differentiation: what is it anyway?
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Differentiation: the chain rule
y=(3 x2+6 x )7
Where has this come from?
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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...
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Compound Angle Formula
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Compound Angle Formula: Key Examples
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We’ll complete this in class!
Double Angle Formula sin 2 A
cos2 A
Half angle formula
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Double/Half Angle Formula: Key examples
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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...
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Factor Formula: Key example
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