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.


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) 30° 45° 60° 90° 180° 270° 360°
Angles (In Radians) π/6 π/4 π/3 π/2 π 3π/2
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

Periodicity Identities (in Radians)

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

Download Trigonometry Formulas PDF


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) = secx/(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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