Trigonometry Formulas - List of Important Trigonometry Formulas

In Mathematics, trigonometry is the most important topic to learn. Trigonometry is basically the study of triangles where ‘Trigon’ means triangle and ‘metry’ means measurement. Also, the trigonometry formulas list is created on the basis of trigonometry ratios such as sine, cosine, and tangent. These formulas are used to solve various trigonometry problems.

Trigonometry formulas list will be helpful for students to solve trigonometric problems easily. Below is the list of formulas based on the right-angled triangle and unit circle which can be used as a reference to study trigonometry.

So the general trigonometry ratios for a right-angled triangle can be written as;
sinθ = OppositesideHypotenuse
cosecθ = HypotenuseOppositeside
Similarly, for a unit circle, for which radius is 1, and θ is the angle.Then,
sinθ = y/1
cosθ = 1/y
tanθ = y/x
cotθ = x/y
secθ = 1/x
cosecθ = 1/y

Trigonometry Identities and Formulas

Tangent and Cotangent Identities
tanθ = sinθcosθ
cotθ = cosθsinθ
Reciprocal Identities
sinθ = 1/cosecθ
cosecθ = 1/sinθ
cosθ = 1/secθ
secθ = 1/cosθ
tanθ = 1/cotθ
cotθ = 1/tanθ
Pythagorean Identities
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ
Even and Odd Formulas
sin(-θ) = -sinθ
cos(-θ) = cosθ
tan(-θ) = -tanθ
cot(-θ) = -cotθ
sec(-θ) = secθ
cosec(-θ) = -cosecθ
Cofunction Formulas
sin(900-θ) = cosθ
cos(900-θ) = sinθ
tan(900-θ) = cotθ
cot(900-θ) = tanθ
sec(900-θ) = cosecθ
cosec(900-θ) = secθ
Formulas for twice of angle
sin2θ = 2 sinθ cosθ
cos2θ = 1 – 2sin2θ
tan2θ = 2tanθ1tan2θ
Half Angle Formulas
sinθ = ±1cos2θ2
cosθ = ±1+cos2θ2
tanθ = ±1cos2θ1+cos2θ
Formulas for Thrice of angle
sin3θ = 3sinθ – 4 sin3θ
Cos 3θ = 4cos3θ – 3 cosθ
Tan 3θ = 3tanθtan3θ13tan2θ
Cot 3θ = cot3θ3cotθ3cot2θ1
The Sum and Difference Formulas
Sin (A+B) = Sin A Cos B + Cos A Sin B
Sin (A-B) = Sin A Cos B – Cos A Sin B
Cos (A+B) = Cos A Cos B – Sin A Sin B
Cos (A-B) = Cos A Cos B + Sin A Sin B
Tan (A+B) = TanA+TanB1TanATanB
Tan (A-B) = TanATanB1+TanATanB
The Product to Sum Formulas
Sin A Sin B = ½ [Cos (A-B) – Cos (A+B)]
Cos A Cos B = ½ [Cos (A-B) + Cos (A+B)]
Sin A Cos B = ½ [Sin (A+B) + Sin (A+B)]
Cos A Sin B = ½ [Sin (A+B) – Sin (A-B)]
The Sum to Product Formulas
Sin A + Sin B = 2 sin A+B2 cos AB2
Sin A – Sin B = 2 cosA+B2 sin AB2
Cos A + Cos B = 2 cosA+B2 cos AB2
Cos A – Cos B = – 2 sinA+B2 sin AB2
Inverse Trigonometric Functions
If Sin θ = x, then θ = sin-1 x = arcsin(x)
Similarly,
θ = cos-1x = arccos(x)
θ = tan-1 x = arctan(x)
Also, the inverse properties could be defined as;
sin-1(sin θ) = θ
cos-1(cos θ) = θ
tan-1(tan θ) = θ