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# Trigonometry Formulas | [PDF] Trigonometry Formula List With Example

Trigonometry Formulas : Well trigonometry is a very small thing. But if we talk about Maths subject then in that case Trigonometry is considered as the most important chapter. And it often happens that with trigonometry you will get to see the questions in your exam.

That is why understanding trigonometry has become very important. In this post we are going to give you all the formulas related to trigonometry in this post. And also we have provided you Trigonometry Formula PDF in this post. From where you can easily Download Trigonometry Formula PDF.

Summary Of Article

## Trigonometry Formulas

In Trigonometry, various sorts of issues can be settled utilizing geometry recipes. These issues may incorporate mathematical proportions (sin, cos, tan, sec, cosec, and bed), Pythagorean characters, item personalities, and so forth A few equations remembering the indication of proportions for various quadrants, including co-work characters (moving points), aggregate and contrast personalities, twofold point personalities, half-point personalities, and so on are additionally given in short here.

There are colossal employments of geometry and its formulae. For instance, the method of triangulation is utilized in Geography to gauge the distance between milestones; in Astronomy, to quantify the distance to close stars and furthermore in satellite route frameworks.

## Trigonometry Formulas List

At the point when we find out about geometrical equations, we consider them for right-calculated triangles as it were. In a right-calculated triangle, we have 3 sides specifically – Hypotenuse, Opposite side (Perpendicular), and Adjacent side (Base). The longest side is known as the hypotenuse, the side inverse to the point is opposite and the side where both hypotenuse and inverse side rests is the contiguous side.

Here is the list of formulas for trigonometry.

 Basic Formulas Reciprocal Identities Trigonometry Table Periodic Identities Co-function Identities Sum and Difference Identities Double Angle Identities Triple Angle Identities Half Angle Identities Product Identities Sum to Product Identities Inverse Trigonometry Formulas

## Basic Trigonometric Function Formulas

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

Reciprocal Identities

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

## Trigonometry Table

 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 ∞ csc ∞ 2 √2 2/√3 1 ∞ -1 ∞ sec 1 2/√3 √2 2 ∞ -1 ∞ 1

 sin (2π – A) = – sin A & cos (2π – A) = cos A sin (2π + A) = sin A & cos (2π + A) = cos A sin (3π/2 – A)  = – cos A & cos (3π/2 – A)  = – sin A sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A sin (π – A) = sin A &  cos (π – A) = – cos A sin (π + A) = – sin A & cos (π + A) = – cos A sin (π/2 – A) = cos A & cos (π/2 – A) = sin A sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A

## Trigonometry Formulas PDF – Trigonometry All Formula

Co-function Identities (in Degrees)

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

Sum & Difference Identities

 cos(x+y) = cos(x)cos(y)–sin(x)sin(y) cos(x–y) = cos(x)cos(y) + sin(x)sin(y) sin(x+y) = sin(x)cos(y)+cos(x)sin(y) sin(x–y) = sin(x)cos(y)–cos(x)sin(y) tan(x+y) = (tan x + tan y)/ (1−tan x •tan y) tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)

Double Angle Identities

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

Triple Angle Identities

 Cos 3x = 4cos3x-3cos x Sin 3x = 3sin x – 4sin3x Tan 3x = [3tanx-tan3x]/[1-3tan2x]

Inverse Trigonometry Formulas

 cos-1 (–x) = π – cos-1 x cosec-1 (–x) = – cosec-1 x cot-1 (–x) = π – cot-1 x sec-1 (–x) = π – sec-1 x sin-1 (–x) = – sin-1 x tan-1 (–x) = – tan-1 x

What is Sin 3x Formula?

Sin 3x is the sine of three times of an angle in a right-angled triangle, that is expressed as:

Sin 3x = 3sin x – 4sin3x

### Conclusion

Here we have given you information about all the formulas related to trigonometry. And also we have provided you here Trigonometry Formula in PDF. If you still have any problem related to this post then let us know by commenting.

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