Source: https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-3-angle-addition-formulae [Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [A Level](https://senecalearning.com/en-gb/revision-notes/a-level.md) › [Maths](https://senecalearning.com/en-gb/revision-notes/a-level/maths.md) › [Edexcel](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel.md) › Angle Addition Formulae # Angle Addition Formulae Maths: Edexcel A Level Pure Maths, topic 5.4.3 ## Angle Addition Formulae Finding the exact value of the sine, cosine, or tangent of an angle is often easier if we can rewrite the given angle in terms of two angles that have known trigonometric values. ### Sine ![Sine](https://image-v2.cdn.app.senecalearning.com/2020-06/186c2602-a62b-4687-8238-c6a1f8ab410d/Screenshot%202020-06-18%20at%2012.41.14-min.png) - We can write the sine of the sum of two angles $$A$$ and $$B$$ using the following identity: - $$\sin(A+B) \equiv \sin A\cos B + \cos A\sin B$$ - We can write the cosine of the sum of two angles $$A$$ and $$B$$ using the following identity: - $$\cos(A+B) \equiv \cos A\cos B -\sin A\sin B$$ ### Proof ![Proof](https://image-v2.cdn.app.senecalearning.com/2020-06/a82053c2-788d-419c-b245-f80be7ad9b94/Screenshot%202020-06-18%20at%2012.41.17-min.png) - Consider two right-angled triangles stacked on top of each other as shown. - The upper triangle (triangle 1) has a hypotenuse equal to 1, with the left corner angle equal to $$A$$ - The lower triangle (triangle 2) has a left corner angle equal to $$B$$ ### Label triangle 1 ![Label triangle 1](https://image-v2.cdn.app.senecalearning.com/2020-06/eff2f77f-6138-45d4-a413-08576d4fb1c4/Screenshot%202020-06-18%20at%2012.41.23-min.png) - Using the fact that the hypotenuse is 1 and the left corner angle is $$A$$, we can label the sides of the upper triangle using trigonometry: - Adjacent = hypotenuse $$\times\cos(\text{angle}) = \cos A$$ - Opposite = hypotenuse $$\times\sin(\text{angle}) = \sin A$$ ### Label triangle 2 ![Label triangle 2](https://image-v2.cdn.app.senecalearning.com/2020-06/062d57a4-d3b6-49cd-8db2-c89a882d21c1/Screenshot%202020-06-18%20at%2012.41.26-min.png) - Using the fact that the hypotenuse is $$\cos A$$ and the left corner angle is $$B$$, we can label the sides of the lower triangle using trigonometry: - Adjacent = hypotenuse $$\times\cos(\text{angle})= \cos A\cos B $$ - Opposite = hypotenuse $$\times\sin(\text{angle})=\cos A\sin B$$ ### Triangle 3 ![Triangle 3](https://image-v2.cdn.app.senecalearning.com/2020-06/67b40942-0db6-4a50-a13c-d78224fc4ff7/Screenshot%202020-06-18%20at%2012.55.30-min.png) - Notice that the hypotenuse of triangle 1 forms another right-angled triangle with angle $$A+B$$. By trigonometry: - Adjacent = $$\cos(A+B)$$ - Opposite = $$\sin(A+B)$$ ### Find angles of triangle 4 ![Find angles of triangle 4](https://image-v2.cdn.app.senecalearning.com/2020-06/0b9c1fae-e1c5-45c5-beeb-4bb4de3373f4/Screenshot%202020-06-18%20at%2012.51.07-min.png) - Triangle 4 is formed by the opposite side of triangle 1 as shown. - By alternate angle theorem, the angle beneath triangle 4 is equal $$B$$. - This means the right corner angle of triangle 4 is equal to 90 $$- B$$. - So the top corner angle is equal to $$B$$. ### Find sides of triangle 4 ![Find sides of triangle 4](https://image-v2.cdn.app.senecalearning.com/2020-06/f893279f-7b9b-4b4f-9e89-23acaa2b3109/Screenshot%202020-06-18%20at%2012.41.28-min.png) - The hypotenuse of triangle 4 is $$\sin A$$. By trigonometry: - Opposite = hypotenuse $$\times \cos(\text{angle}) = \sin A \cos B$$ - Adjacent = hypotenuse $$\times \sin(\text{angle}) = \sin A \sin B$$ ### Find opposite side of triangle 3 ![Find opposite side of triangle 3](https://image-v2.cdn.app.senecalearning.com/2020-06/6f65863c-0ca1-43eb-bc7c-4ef0e837c557/Screenshot%202020-06-18%20at%2012.41.31-min.png) - The length of the opposite side of triangle 3 is equal to: - Opposite = $$\sin(A+B) = \sin A \cos B + \cos A\sin B$$ - Which is the angle addition formula for sine. ### Find adjecent side of triangle 3 ![Find adjecent side of triangle 3](https://image-v2.cdn.app.senecalearning.com/2020-06/7033afd7-8974-4fab-99de-826c5c92d59a/Screenshot%202020-06-18%20at%2013.26.55-min.png) - The length of the adjacent side of triangle 3 is equal to: - Opposite = $$\cos(A+B) = \cos A \cos B - \sin A\sin B$$ - Which is the angle addition formula for cosine. ## Test yourself on Angle Addition Formulae - What is the following expression equivalent to? $$\sin45\cos60+\sin60\cos45$$ - What is the following expression equivalent to? $$\cos116\cos25-\sin116\sin25$$ - What is the following expression equivalent to? $$\cos9\cos75-\sin9\sin75$$ - What is the following expression equivalent to? $$\sin32\cos51+\cos32\sin51$$ [Practise this topic for free](https://app.senecalearning.com/classroom/course/2f7e3897-8547-4e08-b6f9-bbefc48a9d18/section/352b6422-8882-4aa6-a09b-5a2394238a00/session) - Previous topic: [5.4.2 Pythagorean Identities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-2-pythagorean-identities.md) - Next topic: [5.4.4 Manipulating the Angle Addition Formulae](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-4-manipulating-the-angle-addition-formulae.md) ## Maths: Edexcel A Level Pure Maths contents ### 1 Proof - 1.1 Types of Numbers - [1.1.1 Whole Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-1-whole-numbers.md) - [1.1.2 The Four Rules for Positive Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-2-the-four-rules-for-positive-numbers.md) - [1.1.3 Negative Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-3-negative-numbers.md) - [1.1.4 Integers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-4-integers.md) - [1.1.5 The Four Rules for Negative Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-5-the-four-rules-for-negative-numbers.md) - [1.1.6 Real Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-6-real-numbers.md) - [1.1.7 Rational vs Irrational](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-1-7-rational-vs-irrational.md) - 1.2 Notation - [1.2.1 Sets](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-2-1-sets.md) - [1.2.2 Subsets](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-2-2-subsets.md) - [1.2.3 Venn Diagrams](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-2-3-venn-diagrams.md) - [1.2.4 Sets Numbers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-2-4-sets-numbers.md) - [1.2.5 Notation in Mathematical Arguments](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-2-5-notation-in-mathematical-arguments.md) - 1.3 Proof - [1.3.1 Mathematical Proof](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-1-mathematical-proof.md) - [1.3.2 Proof by Deduction](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-2-proof-by-deduction.md) - [1.3.3 Proving an Identity](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-3-proving-an-identity.md) - [1.3.4 Polynomial Identities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-4-polynomial-identities.md) - [1.3.5 Proof by Exhaustion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-5-proof-by-exhaustion.md) - [1.3.6 Disproof by Counter Example](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-6-disproof-by-counter-example.md) - [1.3.7 Proof by Contradiction (A2 Only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/1-3-7-proof-by-contradiction-a2-only.md) ### 2 Algebra & Functions - 2.1 Powers & Roots - [2.1.1 Exponential Rules](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-1-1-exponential-rules.md) - [2.1.2 Rational Exponents](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-1-2-rational-exponents.md) - [2.1.3 Surds](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-1-3-surds.md) - [2.1.4 Simplify Surds](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-1-4-simplify-surds.md) - [2.1.5 Rationalise Denominator](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-1-5-rationalise-denominator.md) - 2.2 Quadratic Equations - [2.2.1 Quadratic +/-](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-1-quadratic.md) - [2.2.2 Factorise Quadratics](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-2-factorise-quadratics.md) - [2.2.3 Quadratic Formula](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-3-quadratic-formula.md) - [2.2.4 Complete the Square](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-4-complete-the-square.md) - [2.2.5 Solve Quadratics Graphically](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-5-solve-quadratics-graphically.md) - [2.2.6 Simultaneous Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-6-simultaneous-equations.md) - [2.2.7 Simultaneous Quadratic Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-7-simultaneous-quadratic-equations.md) - [2.2.8 Simultaneous Equations Graphs](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-8-simultaneous-equations-graphs.md) - [2.2.9 Simultaneous Equations Word Problems](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-9-simultaneous-equations-word-problems.md) - [2.2.10 Quadratic Equations of Powers](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-2-10-quadratic-equations-of-powers.md) - 2.3 Inequalities - [2.3.1 Solving Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-1-solving-inequalities.md) - [2.3.2 Solving Double Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-2-solving-double-inequalities.md) - [2.3.3 Solving Quadratic Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-3-solving-quadratic-inequalities.md) - [2.3.4 Representing Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-4-representing-inequalities.md) - [2.3.5 Graphing Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-5-graphing-inequalities.md) - [2.3.6 Set Notation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-6-set-notation.md) - [2.3.7 Set Notation & Inequalities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-3-7-set-notation-and-inequalities.md) - 2.4 Polynomials - [2.4.1 Polynomials](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-4-1-polynomials.md) - [2.4.2 Adding & Subtracting Polynomials](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-4-2-adding-and-subtracting-polynomials.md) - [2.4.3 Remainder Theorem](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-4-3-remainder-theorem.md) - [2.4.4 Algebraic Long Division](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-4-4-algebraic-long-division.md) - [2.4.5 Rewriting Rational Expressions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-4-5-rewriting-rational-expressions.md) - 2.5 Graphs - [2.5.1 Graphs of Polynomials](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-1-graphs-of-polynomials.md) - [2.5.2 Simultaneous Equations Graphs](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-2-simultaneous-equations-graphs.md) - [2.5.3 Simultaneous Quadratic Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-3-simultaneous-quadratic-equations.md) - [2.5.4 Graphs of Proportion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-4-graphs-of-proportion.md) - [2.5.5 Graphs of Common Functions 1](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-5-graphs-of-common-functions-1.md) - [2.5.6 Graphs of Common Functions 2](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-6-graphs-of-common-functions-2.md) - [2.5.7 Graphs of Common Functions 3](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-7-graphs-of-common-functions-3.md) - [2.5.8 Proportion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-8-proportion.md) - [2.5.9 Direct Proportion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-9-direct-proportion.md) - [2.5.10 Inverse Proportion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-5-10-inverse-proportion.md) - 2.6 Functions - [2.6.1 Properties of Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-6-1-properties-of-functions.md) - [2.6.2 Inverse Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-6-2-inverse-functions.md) - [2.6.3 Composite Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-6-3-composite-functions.md) - 2.7 Transformation of Graphs - [2.7.1 Reflections](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-1-reflections.md) - [2.7.2 Rotation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-2-rotation.md) - [2.7.3 Translation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-3-translation.md) - [2.7.4 Stretches & Compressions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-4-stretches-and-compressions.md) - [2.7.5 Effects of Transformations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-5-effects-of-transformations.md) - [2.7.6 Combinations of Transformations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-7-6-combinations-of-transformations.md) - 2.8 Partial Fractions (A2 Only) - [2.8.1 Partial Fractions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-8-1-partial-fractions.md) - [2.8.2 Partial Fractions with Three Linear Factors](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-8-2-partial-fractions-with-three-linear-factors.md) - [2.8.3 Partial Fractions with Three Linear Factors 2](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-8-3-partial-fractions-with-three-linear-factors-2.md) - [2.8.4 Partial Fractions with Repeated Factors](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-8-4-partial-fractions-with-repeated-factors.md) - [2.8.5 Partial Fractions - Practice](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/2-8-5-partial-fractions-practice.md) ### 3 Coordinate Geometry - 3.1 Straight Lines - [3.1.1 y = mx +c](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-1-1-y-=-mx-c.md) - [3.1.2 Gradient & Y-intercept](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-1-2-gradient-and-y-intercept.md) - [3.1.3 Distance-Time Graph](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-1-3-distance-time-graph.md) - [3.1.4 Velocity-Time Graph](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-1-4-velocity-time-graph.md) - [3.1.5 Conversion Graph](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-1-5-conversion-graph.md) - 3.2 Circles - [3.2.1 Equations of Circles centred at Origin](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-1-equations-of-circles-centred-at-origin.md) - [3.2.2 Finding the Centre & Radius](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-2-finding-the-centre-and-radius.md) - [3.2.3 Equation of a Tangent](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-3-equation-of-a-tangent.md) - [3.2.4 Circle Theorems - Perpendicular Bisector](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-4-circle-theorems-perpendicular-bisector.md) - [3.2.5 Circle Theorems - Angle at the Centre](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-5-circle-theorems-angle-at-the-centre.md) - [3.2.6 Circle Theorems - Angle at a Semi-Circle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-6-circle-theorems-angle-at-a-semi-circle.md) - [3.2.7 Equation of a Perpendicular Bisector](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-7-equation-of-a-perpendicular-bisector.md) - [3.2.8 Equation of a Circumcircle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-8-equation-of-a-circumcircle.md) - [3.2.9 Circumcircle of a Right-angled Triangle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-2-9-circumcircle-of-a-right-angled-triangle.md) - 3.3 Parametric Equations (A2 only) - [3.3.1 Parametric Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-3-1-parametric-equations.md) - [3.3.2 Modelling with Parametric Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/3-3-2-modelling-with-parametric-equations.md) ### 4 Sequences & Series - 4.1 Binomial Expansion - [4.1.1 Pascal's Triangle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-1-1-pascals-triangle.md) - [4.1.2 Factorials](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-1-2-factorials.md) - [4.1.3 Binomial Expansion](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-1-3-binomial-expansion.md) - [4.1.4 Binomial Expansion & Rational Powers (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-1-4-binomial-expansion-and-rational-powers-a2-only.md) - [4.1.5 Binomial Expansion & Rational Powers 2 (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-1-5-binomial-expansion-and-rational-powers-2-a2-only.md) - 4.2 Sequences (A2 only) - [4.2.1 Nth term Rules](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-1-nth-term-rules.md) - [4.2.2 Recurring Rules](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-2-recurring-rules.md) - [4.2.3 Types of Sequences](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-3-types-of-sequences.md) - [4.2.4 Arithmetic Sequences](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-4-arithmetic-sequences.md) - [4.2.5 Geometric Sequences](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-5-geometric-sequences.md) - [4.2.6 Sigma Notation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-6-sigma-notation.md) - [4.2.7 Arithmetic Series](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-7-arithmetic-series.md) - [4.2.8 Geometric Series](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-8-geometric-series.md) - [4.2.9 Sum to Infinity of a Geometric Series](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-9-sum-to-infinity-of-a-geometric-series.md) - [4.2.10 Modelling with Sequences & Series](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/4-2-10-modelling-with-sequences-and-series.md) ### 5 Trigonometry - 5.1 Using Angles - [5.1.1 Radians](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-1-1-radians.md) - [5.1.2 Arc length](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-1-2-arc-length.md) - [5.1.3 Area of Sectors](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-1-3-area-of-sectors.md) - [5.1.4 Area of Segments](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-1-4-area-of-segments.md) - 5.2 Trigonometric Functions - [5.2.1 Unit Circle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-1-unit-circle.md) - [5.2.2 Properties of Trig Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-2-properties-of-trig-functions.md) - [5.2.3 Trigonometry](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-3-trigonometry.md) - [5.2.4 Exact values](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-4-exact-values.md) - [5.2.5 Graphs of Trigonometric Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-5-graphs-of-trigonometric-functions.md) - [5.2.6 Small Angle Approximation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-2-6-small-angle-approximation.md) - 5.3 Triangle Rules - [5.3.1 Sine Rules](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-3-1-sine-rules.md) - [5.3.2 Cosine Rules](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-3-2-cosine-rules.md) - [5.3.3 Area of a Triangle](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-3-3-area-of-a-triangle.md) - 5.4 Trigonometric Identities - [5.4.1 Secant, Cosecant & Cotangent](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-1-secant-cosecant-and-cotangent.md) - [5.4.2 Pythagorean Identities](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-2-pythagorean-identities.md) - [5.4.3 Angle Addition Formulae](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-3-angle-addition-formulae.md) - [5.4.4 Manipulating the Angle Addition Formulae](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-4-manipulating-the-angle-addition-formulae.md) - [5.4.5 Double Angle Formula](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/5-4-5-double-angle-formula.md) ### 6 Exponentials & Logarithms - 6.1 Exponentials & Logarithms - [6.1.1 Exponential Function](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-1-1-exponential-function.md) - [6.1.2 Logarithms](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-1-2-logarithms.md) - [6.1.3 Properties of Logarithms](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-1-3-properties-of-logarithms.md) - [6.1.4 Natural Logarithm](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-1-4-natural-logarithm.md) - [6.1.5 Graphs of Exponents & Logarithms](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-1-5-graphs-of-exponents-and-logarithms.md) - 6.2 Exponential Growth Decay - [6.2.1 Population Growth](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-1-population-growth.md) - [6.2.2 Depreciation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-2-depreciation.md) - [6.2.3 Graphing Linear and Exponential Growth](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-3-graphing-linear-and-exponential-growth.md) - [6.2.4 Interpreting Exponential Growth and Decay Graphs](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-4-interpreting-exponential-growth-and-decay-graphs.md) - [6.2.5 Compound Growth & Decay](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-5-compound-growth-and-decay.md) - [6.2.6 Compund Interest](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/6-2-6-compund-interest.md) ### 7 Differentiation - 7.1 Derivatives - [7.1.1 Gradient of a Curve](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-1-gradient-of-a-curve.md) - [7.1.2 Differentiation from First Principles](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-2-differentiation-from-first-principles.md) - [7.1.3 Differentiation from First Principles - Practice](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-3-differentiation-from-first-principles-practice.md) - [7.1.4 Differentiation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-4-differentiation.md) - [7.1.5 Finding derivatives](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-5-finding-derivatives.md) - [7.1.6 Second Order Derivatives](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-1-6-second-order-derivatives.md) - 7.2 Graphs & Differentiation - [7.2.1 Stationary Points](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-2-1-stationary-points.md) - [7.2.2 Maxima & Minima](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-2-2-maxima-and-minima.md) - [7.2.3 Modelling with Differentiation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-2-3-modelling-with-differentiation.md) - [7.2.4 Using Second Derivatives (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-2-4-using-second-derivatives-a2-only.md) - [7.2.5 Rate of Change (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-2-5-rate-of-change-a2-only.md) - 7.3 Differentiation With Trigonometry and Exponentials - [7.3.1 Differentiation with Sin & Cos](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-3-1-differentiation-with-sin-and-cos.md) - [7.3.2 Diff. of Exponential Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-3-2-diff-of-exponential-functions.md) - [7.3.3 Differentiation of Trig. Functions 1 (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-3-3-differentiation-of-trig-functions-1-a2-only.md) - [7.3.4 Differentiation of Trig. Functions 2 (A2 only)](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-3-4-differentiation-of-trig-functions-2-a2-only.md) - 7.4 Rules of Differetiation (A2 only) - [7.4.1 Chain Rule](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-4-1-chain-rule.md) - [7.4.2 Product Rule](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-4-2-product-rule.md) - [7.4.3 Quotient Rule](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-4-3-quotient-rule.md) - 7.5 Parametric & Implicit Differentiation - [7.5.1 Parametric Differentiation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-5-1-parametric-differentiation.md) - [7.5.2 Implicit Differentiation](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/7-5-2-implicit-differentiation.md) ### 8 Integration - 8.1 Integration - [8.1.1 Integration - Basics](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-1-integration-basics.md) - [8.1.2 Integration - Definite Integrals](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-2-integration-definite-integrals.md) - [8.1.3 Finding Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-3-finding-functions.md) - [8.1.4 Area under curves](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-4-area-under-curves.md) - [8.1.5 Area under x-axis](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-5-area-under-x-axis.md) - [8.1.6 Area between curves and lines](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-1-6-area-between-curves-and-lines.md) - 8.2 Integration (A2 Only) - [8.2.1 Integration - Standard Functions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-1-integration-standard-functions.md) - [8.2.2 Integration - Reverse Chain Rule](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-2-integration-reverse-chain-rule.md) - [8.2.3 Integration by Substitution](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-3-integration-by-substitution.md) - [8.2.4 Integration by Parts](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-4-integration-by-parts.md) - [8.2.5 Integration by Parts - Practice](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-5-integration-by-parts-practice.md) - [8.2.6 Integration by Partial Fraction](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-6-integration-by-partial-fraction.md) - [8.2.7 Modelling with Differential Equations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/8-2-7-modelling-with-differential-equations.md) ### 9 Numerical Methods - 9.1 Finding Solutions - [9.1.1 Number Iterations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-1-1-number-iterations.md) - [9.1.2 Iterations to 1 Decimal Places](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-1-2-iterations-to-1-decimal-places.md) - [9.1.3 Iteration Formula](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-1-3-iteration-formula.md) - [9.1.4 Locating Roots](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-1-4-locating-roots.md) - [9.1.5 Newton Raphson Method](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-1-5-newton-raphson-method.md) - 9.2 Finding the Area - [9.2.1 Trapezium Rule](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/9-2-1-trapezium-rule.md) ### 10 Vectors - 10.1 2D Vectors - [10.1.1 Vectors - Magnitude & Direction](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-1-vectors-magnitude-and-direction.md) - [10.1.2 Unit Vectors](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-2-unit-vectors.md) - [10.1.3 Vectors - Algebraic Operations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-3-vectors-algebraic-operations.md) - [10.1.4 Position Vectors](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-4-position-vectors.md) - [10.1.5 Vector Proofs](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-5-vector-proofs.md) - [10.1.6 Vectors Word Questions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-1-6-vectors-word-questions.md) - 10.2 3D Vectors - [10.2.1 3D Vector Magnitude](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-2-1-3d-vector-magnitude.md) - [10.2.2 3D Vectors - Algebraic Operations](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-2-2-3d-vectors-algebraic-operations.md) - [10.2.3 Position Vectors 3D](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-2-3-position-vectors-3d.md) - [10.2.4 3D Vectors Word Questions](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-2-4-3d-vectors-word-questions.md) - 10.3 Vector Proofs - [10.3.1 Coming Soon](https://senecalearning.com/en-gb/revision-notes/a-level/maths/edexcel/10-3-1-coming-soon.md)