Trigonometry formulas.
Trigonometric formula — common mathematical expressions for trigonometric functions that are performed for all values of the argument.
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Trigonometric functions
Pythagorean identity
Sum-Difference formulas
Double angle formulas
Triple angle formulas
Power-reduction formula
Sum (difference) to product formulas
Product to sum (difference) formulas
Tangent half-angle substitution
Trigonometric functions
sin α,
cos α
| tan α = | sin α | , α ≠ | π | + πn, n є Z |
| cos α | 2 |
| cot α = | cos α | , α ≠ π + πn, n є Z |
| sin α |
tan α · cot α = 1
| sec α = | 1 | , α ≠ | π | + πn, n є Z |
| cos α | 2 |
| cosec α = | 1 | , α ≠ π + πn, n є Z |
| sin α |
Pythagorean identity
sin2 α + cos2 α = 1
| 1 + tan2 α = | 1 |
| cos2 α |
| 1 + cot2 α = | 1 |
| sin2 α |
Sum-Difference Formulas
sin(α + β) = sin α · cos β + cos α · sin β
sin(α – β) = sin α · cos β – cos α · sin β
cos(α + β) = cos α · cos β – sin α · sin β
cos(α – β) = cos α · cos β + sin α · sin β
| tan(α + β) = | tan α + tan β |
| 1 – tanα · tan β |
| tan(α – β) = | tan α – tan β |
| 1 + tanα · tan β |
| cot(α + β) = | cotα · cot β - 1 |
| cot β + cot α |
| cot(α - β) = | cotα · cot β + 1 |
| cot β - cot α |
Double angle formulas
sin 2α = 2 sin α · cos α
cos 2α = cos2 α - sin2 α
| tan 2α = | 2 tan α |
| 1 - tan2 α |
| cot 2α = | cot2 α - 1 |
| 2 cot α |
Triple angle formulas
sin 3α = 3 sin α - 4 sin3 α
cos 3α = 4 cos3 α - 3 cos α
| tan 3α = | 3 tan α - tan3 α |
| 1 - 3 tan2 α |
| cot 3α = | 3 cot α - cot3 α |
| 1 - 3 cot2 α |
Power-reduction formula
| sin2 α = | 1 - cos 2α |
| 2 |
| cos2 α = | 1 + cos 2α |
| 2 |
| sin3 α = | 3 sin α - sin 3α |
| 4 |
| cos3 α = | 3 cos α + cos 3α |
| 4 |
Sum (difference) to product formulas
| sin α + sin β = 2 sin | α + β | cos | α - β |
| 2 | 2 |
| sin α - sin β = 2 sin | α - β | cos | α + β |
| 2 | 2 |
| cos α + cos β = 2 cos | α + β | cos | α - β |
| 2 | 2 |
| cos α - cos β = -2 sin | α + β | sin | α - β |
| 2 | 2 |
| tan α + sin β = | sin(α + β) |
| cos α · cos β |
| tan α - sin β = | sin(α - β) |
| cos α · cos β |
| cot α + sin β = | sin(α + β) |
| sin α · sin β |
| cot α - sin β = | sin(α - β) |
| sin α · sin β |
a sin α + b cos α = r sin (α + φ),
| where r2 = a2 + b2, sin φ = | b | , tan φ = | b |
| r | a |
Product to sum (difference) formulas
| sin α · sin β = | 1 | (cos(α - β) - cos(α + β)) |
| 2 |
| sin α · cos β = | 1 | (sin(α + β) + sin(α - β)) |
| 2 |
| cos α · cos β = | 1 | (cos(α + β) + cos(α - β)) |
| 2 |
Tangent half-angle substitution
| sin α = | 2 tan (α/2) |
| 1 + tan2 (α/2) |
| cos α = | 1 - tan2 (α/2) |
| 1 + tan2 (α/2) |
| tan α = | 2 tan (α/2) |
| 1 - tan2 (α/2) |
| cot α = | 1 - tan2 (α/2) |
| 2 tan (α/2) |
Factoring: Some special cases
Formulas and properties of exponents
Formulas and properties of nth root
Formulas and properties of logarithms
Formulas and properties of arithmetic sequence
Formulas and properties of geometrical sequence
Trigonometry formulasDerivative formulas
Integrals table
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