In Trigonometry, different types of troubles can be fixed using trigonometry formulas. These troubles may include trigonometric ratios (sin, cos, tan, sec, cosec and also cot), Pythagorean identities, product identities, etc. Part formulas including the sign of ratios in different quadrants, entailing co-function identities (shifting angles), amount & difference identities, dual angle identities, half-angle identities, etc. Are likewise given in quick here.

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Learning and memorizing these mathematics formulas in trigonometry will assist the student of course 10, 11, and 12 to score an excellent marks in this concept. Castle can uncover the trigonometry table together with inverse trigonometry formulas to deal with the problems based on them.

Trigonometry recipe PDF

Below is the connect given come download the pdf layout of Trigonometry formulas for totally free so that students deserve to learn lock offline too.


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Trigonometry is a branch of math that deals with triangles. Trigonometry is likewise known as the study of relationships in between lengths and angles the triangles.

There is an enormous variety of uses of trigonometry and also its formulae. Because that example, the method of triangulation is offered in location to measure up the distance in between landmarks; in Astronomy, to measure up the distance to adjacent stars and additionally in satellite navigation systems.


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Trigonometry recipe List

When us learn around trigonometric formulas, we take into consideration them because that right-angled triangles only. In a right-angled triangle, we have actually 3 sides namely – Hypotenuse, Opposite side (Perpendicular), and surrounding side (Base). The longest side is well-known as the hypotenuse, the side opposite to the edge is perpendicular and the side wherein both hypotenuse and opposite side rests is the surrounding side.

Here is the perform of formulas for trigonometry.

Basic Trigonometric role Formulas

There room basically 6 ratios supplied for detect the aspects in Trigonometry. Castle are called trigonometric functions. The 6 trigonometric features are sine, cosine, secant, co-secant, tangent and also co-tangent.

By utilizing a right-angled triangle together a reference, the trigonometric functions and also identities are derived:

sin θ = Opposite Side/Hypotenusecos θ = adjacent Side/Hypotenusetan θ = Opposite Side/Adjacent Sidesec θ = Hypotenuse/Adjacent Sidecosec θ = Hypotenuse/Opposite Sidecot θ = Adjacent Side/Opposite Side

Reciprocal Identities

The Reciprocal Identities are offered as:

cosec θ = 1/sin θsec θ = 1/cos θcot θ = 1/tan θsin θ = 1/cosec θcos θ = 1/sec θtan θ = 1/cot θ

All these space taken from a best angled triangle. Once height and base next of the appropriate triangle are known, us can discover out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are likewise derived by making use of the trigonometric functions.

Trigonometry Table

Below is the table because that trigonometry formulas for angles that are generally used for solving problems.


Angles (In Degrees)30°45°60°90°180°270°360°
Angles (In Radians)π/6π/4π/3π/2π3π/2
sin01/21/√2√3/210-10
cos1√3/21/√21/20-101
tan01/√31√300
cot√311/√300
csc2√22/√31-1
sec12/√3√22-11

Periodicity Identities (in Radians)

These formulas are offered to transition the angles by π/2, π, 2π, etc. Lock are also called co-function identities.

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

All trigonometric identities space cyclic in nature. Lock repeat themselves after this periodicity constant. This periodicity consistent is various for different trigonometric identities. Tan 45° = tan 225° yet this is true because that cos 45° and also cos 225°. Refer to the over trigonometry table come verify the values.

Co-function Identities (in Degrees)

The co-function or regular identities can additionally be stood for in degrees as:

sin(90°−x) = cos xcos(90°−x) = sin xtan(90°−x) = cot xcot(90°−x) = tan xsec(90°−x) = csc xcsc(90°−x) = sec x

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)

Double edge 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) = sec2 x/(2-sec2 x)csc (2x) = (sec x. Csc x)/2

Triple edge Identities

Sin 3x = 3sin x – 4sin3xCos 3x = 4cos3x-3cos xTan 3x = <3tanx-tan3x>/<1-3tan2x>

Half angle Identities

\(\sin\fracx2=\pm \sqrt\frac1-\cos\: x2\)\(\cos\fracx2=\pm \sqrt\frac1+\cos\: x2\)\(\tan(\fracx2) = \sqrt\frac1-\cos(x)1+\cos(x)\)

Also, \(\tan(\fracx2) = \sqrt\frac1-\cos(x)1+\cos(x)\\ \\ \\ =\sqrt\frac(1-\cos(x))(1-\cos(x))(1+\cos(x))(1-\cos(x))\\ \\ \\ =\sqrt\frac(1-\cos(x))^21-\cos^2(x)\\ \\ \\ =\sqrt\frac(1-\cos(x))^2\sin^2(x)\\ \\ \\ =\frac1-\cos(x)\sin(x)\) So, \(\tan(\fracx2) =\frac1-\cos(x)\sin(x)\)

Product identities

\(\sin\: x\cdot \cos\:y=\frac\sin(x+y)+\sin(x-y)2\)\(\cos\: x\cdot \cos\:y=\frac\cos(x+y)+\cos(x-y)2\)\(\sin\: x\cdot \sin\:y=\frac\cos(x-y)-\cos(x+y)2\)

Sum come Product Identities

\(\sin\: x+\sin\: y=2\sin\fracx+y2\cos\fracx-y2\)\(\sin\: x-\sin\: y=2\cos\fracx+y2\sin\fracx-y2\)\(\cos\: x+\cos\: y=2\cos\fracx+y2\cos\fracx-y2\)\(\cos\: x-\cos\: y=-2\sin\fracx+y2\sin\fracx-y2\)

Inverse Trigonometry Formulas

sin-1 (–x) = – sin-1 xcos-1 (–x) = π – cos-1 xtan-1 (–x) = – tan-1 xcosec-1 (–x) = – cosec-1 xsec-1 (–x) = π – sec-1 xcot-1 (–x) = π – cot-1 x

What is Sin 3x Formula?

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

Sin 3x = 3sin x – 4sin3x

Trigonometry recipe From class 10 to class 12


Trigonometry formulas For course 12
Trigonometry formulas For course 11
Trigonometry recipe For course 10

Trigonometry Formulas major systems

All trigonometric recipe are divided into two significant systems:

Trigonometric IdentitiesTrigonometric Ratios

Trigonometric Identities room formulas the involve Trigonometric functions. These identities space true because that all values of the variables. Trigonometric proportion is known for the relationship between the measurement of the angles and the length of the political parties of the appropriate triangle.

Here we provide a list of every Trigonometry formulas for the students. This formulas are helpful for the students in resolving problems based on these formulas or any trigonometric application. In addition to these, trigonometric identities help us to have the trigonometric formulas, if lock will appear in the examination.

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We also provided the straightforward trigonometric table pdf that gives the relation of every trigonometric functions in addition to their typical values. This trigonometric formulae are valuable in identify the domain, range, and also value of a link trigonometric function. Students deserve to refer to the formulas detailed below or can also download the trigonometric formulas pdf that is noted above.