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.


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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 )
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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Trigonometry Notes
Sine Rule:
The sine rule is defined as follows;
A = sinB C sinA = sinB sinC
sin A B = sin C or A B = C
It is used to describe the relationship between the three angles in any triangle, and their opposing
sides, although if a right-angled triangle is present, it is more efficient to use one of the three basic
ratios in order to work out the values of any sides or angles given two pieces of information.…read more

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Trigonometry Notes
Compound Angle Formulae:
sin (A + B) = sin A cos B + cos A sin B or sin (A - B) = sin A cos B - cos A sin B
For the sine compound angles, the operation sign in between A and B is the same (in red) and the
sines are mixed with cosines (in green).…read more

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Trigonometry Notes
R- Formulae and Method:
Expressions in the form asin ±bcos or acos ±bsin can be expressed in the forms
Rsin (±) or Rcos (±) respectively as follows;
asin ±bcos Rsin (±) , with R > 0 , and 0 < < 90° (or 2rad)
acos ±bsin Rcos (±) , with R > 0 , and 0 < < 90° (or 2rad)
Where Rcos = a, and Rsin = b, and R = a2 + b2
To find , Rsin (±) or Rcos (±)…read more

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Trigonometry Notes
Factor Formulae:
These formulae are useful in to help put an equation involving sines or cosines multiplying by either
themselves or each other into an easier form to integrate.…read more


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