# Core 1-4 Trigonometry Notes

These are notes that I have made myself, covering all the Trigonometry needed in C1, C2, C3, and C4. My exam board is Edexcel, but all the things included in here are transferable to the other exam boards.

Formulas to remember have been highlighted, and there are also derivations for some of the things necessary to know.

Topics covered are; Basic Trigonometric Ratios (circular functions), Sine Rule, Cosine Rule, Inverse Trigonometric Functions, Pythagorus' Theorem, Reciprocal Functions, Pythagorean Identities, Compound Angle Formulae, Double Angle Formulae, R-alpha method, Half-Angle Formulae, and Factor Formulae.

THERE ARE NO WORKED THROUGH EXAMPLE QUESTIONS, ALTHOUGH THE R-ALPHA METHOD HAS BEEN WORKED THROUGH ALGREBRAICALLY.

- Created by: Kwok Wei Lee
- Created on: 31-05-12 19:52

First 259 words of the document:

Trigonometry Notes

C1, C2, C3 and C4 Notes and Formulas

Trigonometric Identities

Basic Trigonometric Ratios: sin = O A O

H cos = H tan = A

where O is the side Opposite angle ; A is the side Adjacent to angle ; and H is the Hypotenuse

(the side opposite the right-angle.

These three ratios are the foundation for trigonometry, and they describe the relationships

between the sides in a right-angled triangle, and a corresponding angle.

Additional Definition for tan : sin

tan cos

Proof is as follows;

sin = (OH) O H

RHS : cos A = H× A

(H )

=O

A = tan = LHS

Inverse Functions of Trigonometric Ratios:

sin-1 = arcsincosec {domain :- 1x1}{range :-

2arcsin 2}

cos-1 = arccos sec {domain :- 1x1}{range : 0arccos }

tan-1 = arctancot {domain : xR}{range :-

2arctan 2 }

These inverse functions can be used to work out the value of as follows;

= sin-1 ( O -1 A -1 O

H ) = cos ( H ) = tan ( A )

Pythagorus' Theorem:

Pythagorus' theorem states that the square of the Hypotenuse of a right-angled triangle is

equivalent to the sum of the squares of the other corresponding sides. That is;

a2 + b2 = c2

where c is the hypotenuse and a and b are the other sides.

This is a useful rule to use when given the values of two sides of a right-angled triangle, and asked to

calculate the other.

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Joe Lee

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