Trigonometry Formulas - List of Important Trigonometry Formulas

This page gives a quick reference to list of important trigonometry formulas for your reference.

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

cosθ = AdjacentSideHypotenuse

tanθ = OppositesideAdjacentSide

secθ = HypotenuseAdjacentside

cosecθ = HypotenuseOppositeside

cotθ = AdjacentsideSideopposite

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 = 2tanθ1−tan2θ

Half Angle Formulas

sinθ = ±1−cos2θ2−−−−−−√

cosθ = ±1+cos2θ2−−−−−−√

tanθ = ±1−cos2θ1+cos2θ−−−−−−√

Formulas for Thrice of angle

sin3θ = 3sinθ – 4 sin3θ

Cos 3θ = 4cos3θ – 3 cosθ

Tan 3θ = 3tanθ–tan3θ1−3tan2θ

Cot 3θ = cot3θ–3cotθ3cot2θ−1

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+TanB1–TanATanB

Tan (A-B) = TanA–TanB1+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 A−B2

Sin A – Sin B = 2 cosA+B2 sin A−B2

Cos A + Cos B = 2 cosA+B2 cos A−B2

Cos A – Cos B = – 2 sinA+B2 sin A−B2

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