Trigonometry Formulas List

In arithmetic, pure mathematics is the most vital topic to find out. pure mathematics is largely the study of triangles wherever ‘Trigon’ suggests that triangle and ‘metry’ suggests that activity. Also, a pure mathematics formulas list is made on the premise of pure mathematics ratios like trigonometric function, circular function, and tangent. These formulas area unit wont to solve numerous pure mathematics issues.

Taking an associate degree example of the correct angle triangle, a pure mathematics formulas list is created. All the pure mathematics formulas area unit supported pure mathematics identities and pure mathematics ratios. the connection between angles and length of the edges of the Triangle is developed with the assistance of pure mathematics ideas.

Trigonometry formulas list is going to be useful for college kids to resolve pure mathematics issues simply. Below is that the list of formulas supported the triangle and unit circle which may be used as a relation to study pure mathematics.

List of vital pure mathematics Formulas

First allow us to learn basic formulas of pure mathematics, considering a triangle, that has associate degree angle θ, a flank, a facet opposite angle θ and a facet adjacent to angle θ.

 

List of Important Trigonometry Formulas

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 = 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

Values for Trigonometry ratios

Values for Trigonometry ratios:

Degrees

00

300

450

600

900

1800

2700

3600

Radians

0

π/6

π/4

π/3

π/2

π

3π/2

Sinθ

0

1/2

1/2–√ 3–√/2

1

0

-1

0

Cosθ

1

3–√/2 1/2–√

1/2

0

-1

0

1

Tanθ

0

1/3–√

1

3–√

0

0

Cotθ

/3–√

1

1/3–√

0

0

Secθ

1

2/3–√

/2–√

2

-1

1

Cosecθ

2

/2–√

2/3–√

1

-1

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