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Trigonometry formulae

The 16 results the trigonometry notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 16, the formulae booklet prints 4 and 12 are yours to memorise.

Years 12-13 · 5 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

5 lessons

Triangles and the sine and cosine rules

asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}NOT IN THE BOOKLET: LEARN ITConditionsAny triangle. Finding an angle can be ambiguous: the calculator returns the acute value and the obtuse supplement may fit as well.
a2=b2+c2−2bccosAa^{2} = b^{2} + c^{2} − 2bc \cos ANOT IN THE BOOKLET: LEARN ITConditionsAny triangle, with A the angle opposite the side a.
Area=12absinC\text{Area} = \frac{1}{2}ab \sin CNOT IN THE BOOKLET: LEARN ITConditionsC the angle between the two sides a and b.

Trigonometric graphs and equations

tanθ=sinθcosθ\tan θ = \frac{\sin θ}{\cos θ}NOT IN THE BOOKLET: LEARN ITConditionscos θ ≠ 0, so θ is not an odd multiple of 90°.
sin2θ+cos2θ=1\sin^{2} θ + \cos^{2} θ = 1NOT IN THE BOOKLET: LEARN ITConditionsEvery angle θ; no restriction.

Radians, arcs and small angles

s=rθs = rθNOT IN THE BOOKLET: LEARN ITConditionsθ in radians.
A=12r2θA = \frac{1}{2}r^{2}θNOT IN THE BOOKLET: LEARN ITConditionsθ in radians.
sinθ≈θ,cosθ≈1−θ22,tanθ≈θ\sin θ ≈ θ, \, \cos θ ≈ 1 − \frac{θ^{2}}{2}, \, \tan θ ≈ θIN THE FORMULAE BOOKLETConditionsθ small and measured in radians. In degrees all three are false.

Reciprocal and inverse trigonometric functions

sec2θ=1+tan2θ\text{sec}^{2} θ = 1 + \text{tan}^{2} θNOT IN THE BOOKLET: LEARN ITConditionscos θ ≠ 0.
cosec2θ=1+cot2θ\text{cosec}^{2} θ = 1 + \text{cot}^{2} θNOT IN THE BOOKLET: LEARN ITConditionssin θ ≠ 0.

Compound angles and the harmonic form

sin(A±B)=sinAcosB±cosAsinB\sin (A ± B) = \sin A \cos B ± \cos A \sin BIN THE FORMULAE BOOKLETConditionsAll A and B; no restriction.
cos(A±B)=cosAcosB∓sinAsinB\cos (A ± B) = \cos A \cos B ∓ \sin A \sin BIN THE FORMULAE BOOKLETConditionsAll A and B; no restriction.
tan(A±B)=tanA±tanB1∓tanAtanB\tan (A ± B) = \frac{\tan A ± \tan B}{1 ∓ \tan A \tan B}IN THE FORMULAE BOOKLETConditionstan A, tan B and tan(A ± B) must all be defined, and 1 ∓ tan A tan B ≠ 0.
sin2A=2sinAcosA\sin 2A = 2 \sin A \cos ANOT IN THE BOOKLET: LEARN ITConditionsAll A; no restriction.
cos2A=cos2A−sin2A=2cos2A−1=1−2sin2A\cos 2A = \cos^{2}A − \sin^{2}A = 2\cos^{2}A − 1 = 1 − 2\sin^{2}ANOT IN THE BOOKLET: LEARN ITConditionsAll A; no restriction.
tan2A=2tanA1−tan2A\tan 2A = \frac{2\tan A}{1 − \tan^{2}A}NOT IN THE BOOKLET: LEARN ITConditionstan A defined and tan²A ≠ 1.

Every formula in the library is indexed by unit on the equation index, and the trigonometry notes are where these results are derived and used. The 12 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Sequences and series formulae · Exponentials and logarithms formulae