# Trigonometry Math Formulas List

Trigonometry is a department of mathematics that offers with triangles. Trigonometry is also called the study of relationships between lengths and angles of triangles.

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There is a gigantic variety of makes use of of trigonometry and its formulae. For example, the strategy of triangulation is utilized in Geography to measure the distance between landmarks; in Astronomy, to measure the distance to nearby stars and also in satellite navigation systems.

## Trigonometry Functions Formulas

In a right-angled triangle, we’ve three sides particularly – Hypotenuse, Opposite side (Perpendicular) and Adjacent side (Height). The longest side is named the hypotenuse, the side opposite to the angle is perpendicular and the side the place each hypotenuse and opposite side rests is the adjacent side.

There are mainly 6 Laws used for finding the elements in Trigonometry. They are known as trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions or identities are derived:

By using a right-angled triangle as a reference, the trigonometric functions or identities are derived:

• sin θ = Opposite Side / Hypotenuse
• sec θ = Hypotenuse / Adjacent Side
• cos θ = Adjacent Side / Hypotenuse
• tan θ = Opposite Side / Adjacent Side
• cosec θ = Hypotenuse / Opposite Side
• cot θ = Adjacent Side / Opposite Side

The Reciprocal Identities are given as:

• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• cot θ = 1/tan θ
• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ

All these are taken from a right angled triangle. With the length and base side of the right triangle given, we are able to find out the sine, cosine, tangent, secant, cosecant and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are additionally derived by using the trigonometric functions.

## Trigonometry Formulas List

### 1.Trigonometry Formulas involving Periodicity Identities (in Radians)

• sin(x+2πn) = sin x
• cos(x+2πn) = cos x
• tan(x+πn) = tan x
• cot(x+πn) = cot x
• sec(x+2πn) = sec x
• csc(x+2πn) = csc x

where n is an integer.

All trigonometric identities are cyclic in nature. They repeat themselves after this periodicity constant. This periodicity constant is different for different trigonometric identity. tan 45 = tan 225 but this is true for cos 45 and cos 225. Refer to the above trigonometry table to verify the values.

### 2.Trigonometry Formulas involving Cofunction Identities (in Degrees)

• sin(90°−x) = cos x
• cos(90°−x) = sin x
• tan(90°−x) = cot x
• cot(90°−x) = tan x
• sec(90°−x) = csc x
• csc(90°−x) = sec x

### 3.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)]
• cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
• tan(2x) = [2tan(x)]/ [1−tan2(x)]
• sec (2x) = secx/(2-sec2 x)
• csc (2x) = (sec x. csc x)/2

### 4.Trigonometry Formulas involving Sum/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) = (tan x–tan y)/ (1+tan x • tan y)

### 4.Trigonometry Formulas involving Sum to Product Identities:

• sinx+siny = 2sinx + y2cosx − y2
• sinx−siny = 2cosx + y2sinx − y2
• cosx+cosy = 2cosx + y2cosx − y2
• cosx−cosy= −2sinx + y2sinx − y2

### 5.Trigonometry Formulas involving Product identities:

• sinx⋅cosy = sin(x+y) + sin(x−y)2
• cosx⋅cos y= cos(x+y) + cos(x−y)2
• sinx⋅siny = cos(x+y) − cos(x−y)2

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