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# Trigonometry Formula

Trigonometry Formula: Explore more about the Trigonometry Formula with solved examples

## Trigonometry is one of the branches of mathematics that explores the connections between the three sides and the three angles of a triangle.

Six essential trigonometric ratios are used in all of the formulae that pertain to trigonometry. The majority of the formulae used in trigonometry are required to calculate these ratios, also known as trigonometric functions. The six fundamental trigonometric functions are the sine, the cosine, the secant, the cosecant, the tangent, and the cotangent.

## What are all the trigonometric formulas?

Trigonometric formulas may be divided into many distinct groups according to the trigonometric identities  used in the calculations. Let’s have a look at the many different trigonometric formulae that are listed here.

### Basic Trigonometric Formulas

• sin θ = Perpendicular/Hypotenuse

• cos θ = Base/Hypotenuse

• tan θ = Perpendicular/Base

• cot θ = Base/Perpendicular

• cosec θ = Hypotenuse/Perpendicular

• sec θ = Hypotenuse/Base

### Reciprocal Trigonometric Formulas

• sin θ = 1/cosec θ

• cos θ = 1/sec θ

• tan θ = 1/cot θ

• sec θ = 1/cos θ

• cot θ = 1/tan θ

• cosec θ = 1/sin θ

Table for Trigonometric Formulas

 Angles(In Degrees) 0 30 45 60 90 180 270 360 Angles(In Radians) 0 π/6 π/4 π/3 π/2 π 3π/2 2π Sin 0 1/2 1/√2 √3/2 1 0 -1 0 Cos 1 √3/2 1/√2 1/2 0 -1 0 1 Tan 0 1/√3 1 √3 ∞ 0 ∞ 0 Cot ∞ √3 1 1/√3 0 ∞ 0 ∞ Cosec ∞ 2 √2 2/√3 1 ∞ -1 ∞ Sec 1 2/√3 √2 2 ∞ -1 ∞ 1

### Sum and Difference Identities

• sin(x+y)=sin(x)cos(y)+cos(x)sin(y)

• cos(x+y)=cos(x)cos(y)–sin(x)sin(y)

• tan⁡(x+y)=(tan⁡x+tan⁡y) / (1–tan⁡x⋅tan⁡y)

• sin(x–y)=sin(x)cos(y)–cos(x)sin(y)

• cos⁡(x–y)=cos⁡(x)cos⁡(y)+sin⁡(x)sin⁡(y)

• tan(x−y)=(tanx–tany) / (1+tanx∙tany)

Cofunction Identities

• sin(90° − x) = cos x

• cos(90° − x) = sin x

• tan(90° − x) = cot x

• cot(90° − x) = tan x

• sec(90° − x) = cosec x

• cosec(90° − x) = sec x

### Trigonometry Formulas Involving Double Angle Identities

• sin (2x) = 2sin(x) • cos(x) = [2tan x/(1 + tan2 x)]

• cos (2x) = cos2(x) – sin2(x) = [(1 – tan2 x)/(1 + tan2 x)] = 2cos2(x) – 1 = 1 – 2sin2(x)

• tan (2x) = [2tan(x)]/ [1 – tan2(x)]

### Trigonometry Formulas Involving Triple Angle Identities

• sin 3x = 3sin x – 4sin3x

• cos 3x = 4cos3x – 3cos x

## Frequently asked questions

Get answers to the most common queries related to the Trigonometry Formula

## Which Trigonometry Formulas Involve Pythagorean Identities?

Ans : sin2A + cos2A = 1 ...Read full

## How can one best retain trigonometric formulae to memory?

Ans : Become acquainted with mathematical representations. ...Read full