Trigonometry all formulas pdf download:Trigonometry is a branch of mathematics that deal with angles, lengths and heights of triangles and relations between different parts of circles and other geometrical figures. Maths Formulas – Trigonometric Ratios and identities are very useful and learning the below formulae help in solving the problems better. Trigonometry formulas pdf are essential for solving questions in Trigonometry Ratios and Identities in Competitive Exams.
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Details of Page Contents
 1 Trigonometry all Formulas List pdf download
 2 Magical Hexagon for Trigonometry Identities
 3 Reciprocal Identities
 4 Trigonometry Table
 5 Periodicity Identities (in Radians)
 6 Signs of Trigonometric Ratios
 7 Cofunction Identities (in Degrees)
 8 Sum & Difference Identities
 9 Double Angle Identities
 10 Triple Angle Identities
 11 Half Angle Identities
 12 Product identities
 13 Sum to Product Identities
 14 Inverse Trigonometry Formulas
 15 Values of Trigonometric Functions
 16 Important Tips to solve trigonometry questions faster:
 17 Some Important Books for Competitive Exam:
 18 Frequently Asked Questions(FAQ):
 19 Q1: What formulas should I study for the SSC CHSL?
 20 Q2: What are the basic trigonometric ratios?
 21 Q3: What are all the formulas of trigonometry?
 22 Q4: What are formulas for trigonometry ratios?
 23 Q5: How do I memorize maths trigonometry formulas?
 24 Q6: What are the three main functions in trigonometry?
 25 Q7: Can I get a trigonometry formulas list?
 26 Q8: What are the fundamental trigonometry identities?
 27 Q9: Trigonometry formulas are applicable to which triangle?
Trigonometry all Formulas List pdf download
Trigonometric Identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
Trigonometric Ratio relationship between the measurement of the angles and the length of the side of the right triangle. These formulas relate lengths and areas of particular circles or triangles. On the next page you’ll find identities. The identities don’t refer to particular geometric figures but hold for all angles.
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When we learn about trigonometric formulas, we consider it for rightangled triangles only. In a rightangled triangle, we have 3 sides namely – Hypotenuse, Opposite side (Perpendicular), and Adjacent side (Height). The longest side is known as the hypotenuse, the side opposite to the angle is perpendicular and the side where both hypotenuse and opposite side rests is the adjacent side.
Here is the list of formulas for trigonometry.

Basic Formulas

Reciprocal Identities

Trigonometry Table

Periodic Identities

Cofunction Identities

Sum and Difference Identities

Double Angle Identities

Triple Angle Identities

Half Angle Identities

Product Identities

Sum to Product Identities

Inverse Trigonometry Formulas
Download Definition of the Trig Functions
Formulas for arcs and sectors of circles
You can easily find both the length of an arc and the area of a sector for an angle θ in a circle of radius r.
Length of an arc. The length of the arc is just the radius r times the angle θ where the angle is measured in radians. To convert from degrees to radians, multiply the number of degrees by π/180.
Arc = rθ.
Trigonometric all Formulas pdf download – Right Angle
The most important formulas for trigonometry are those for a right triangle. If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.
Pythagorean theorem, the wellknown geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, (P)^{2} + (B)^{2} = (H)^{2}
Applying Pythagoras theorem for the given rightangled theorem, we have:
(Perpendicular)^{2} + (Base)^{2} = (Hypotenuse)^{2}
^{⇒}^{ }(P)^{2} + (B)^{2} = (H)^{2}
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.
By using a rightangled triangle as a reference, the trigonometric functions or identities are derived:

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular
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Magical Hexagon for Trigonometry Identities
Clock Wise:

tan(x) = sin(x) / cos(x)

sin(x) = cos(x) / cot(x)

cos(x) = cot(x) / csc(x)

cot(x) = csc(x) / sec(x)

csc(x) = sec(x) / tan(x)

sec(x) = tan(x) / sin(x)
Counter clock Wise:

cos(x) = sin(x) / tan(x)

sin(x) = tan(x) / sec(x)

tan(x) = sec(x) / csc(x)

sec(x) = csc(x) / cot(x)

csc(x) = cot(x) / cos(x)

cot(x) = cos(x) / sin(x)
Reciprocal Identities
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
Trigonometry all Formulas pdf download Download
All these are taken from a right angled triangle. With the length and base side of the right triangle given, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.
Trigonometry Table
Below is the table for trigonometry formulas for angles that are commonly used for solving problems.
Periodicity Identities (in Radians)
These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called cofunction identities.

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

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

sin (2π + A) = sin A & cos (2π + A) = cos A
All trigonometric identities are cyclic in nature. They repeat themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is true for cos 45° and cos 225°. Refer to the above trigonometry table to verify the values.
Signs of Trigonometric Ratios
Cofunction Identities (in Degrees)
The cofunction or periodic identities can also be represented in degrees as:
 sin(π/2−θ) = cosθ
 cos(π/2−θ) = sinθ
 tan(π/2−θ) = cotθ
 cot(π/2−θ) = tanθ
 sec(π/2−θ) = cosecθ
 cosec(π/2−θ) = secθ
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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)
Trigonometry all Formulas pdf download Part 1
Double Angle Identities

sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan^{2} x)]

cos(2x) = cos^{2}(x)–sin^{2}(x) = [(1tan^{2} x)/(1+tan^{2} x)]

cos(2x) = 2cos^{2}(x)−1 = 1–2sin^{2}(x)

tan(2x) = [2tan(x)]/ [1−tan^{2}(x)]

sec (2x) = sec^{2 }x/(2sec^{2} x)

csc (2x) = (sec x. csc x)/2
Trigonometry all Formulas pdf download Part 2
Triple Angle Identities

Sin 3x = 3sin x – 4sin^{3}x

Cos 3x = 4cos^{3}x3cos x

Tan 3x = [3tanxtan^{3}x]/[13tan^{2}x]
Half Angle Identities
$\mathrm{sin}\frac{x}{2}=\pm \sqrt{\frac{1\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}x}{2}}$
$\mathrm{cos}\frac{x}{2}=\pm \sqrt{\frac{1+\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}x}{2}}$
Product identities
$\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}x\cdot \mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}y=\frac{\mathrm{sin}(x+y)+\mathrm{sin}(xy)}{2}$
$\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}x\cdot \mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}y=\frac{\mathrm{cos}(x+y)+\mathrm{cos}(xy)}{2}$
$\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}x\cdot \mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}y=\frac{\mathrm{cos}(xy)\mathrm{cos}(x+y)}{2}$
Sum to Product Identities
$\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}x+\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}y=2\mathrm{sin}\frac{x+y}{2}\mathrm{cos}\frac{xy}{2}$
$\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}x\mathrm{sin}\phantom{\rule{mediummathspace}{0ex}}y=2\mathrm{cos}\frac{x+y}{2}\mathrm{sin}\frac{xy}{2}$
$\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}x+\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}y=2\mathrm{cos}\frac{x+y}{2}\mathrm{cos}\frac{xy}{2}$
Inverse Trigonometry Formulas
 sin^{1} (–x) = – sin^{1} x
 cos^{1} (–x) = π – cos^{1} x
 tan^{1} (–x) = – tan^{1} x
 cosec^{1} (–x) = – cosec^{1} x
 sec^{1} (–x) = π – sec^{1} x
 cot^{1} (–x) = π – cot^{1} x
Values of Trigonometric Functions
Important Tips to solve trigonometry questions faster:
1. Always try to bring the multiple angles to single angles using basic formula. Make sure all your angles are the same.
Using and is difficult, but if you use , that leaves and , and now all your functions match.
The same goes for addition and subtraction: don’t try working with and . Instead, use
So that all the angles match.
2. Converting to sin and cos all the items in the problem using basic formula. I have mentioned sin and cos as they are easy to solve. You can use any other also.
3. Use Pythagorean identifies to simplify the equations
4. Check all the angles for sums and differences and use the appropriate identities to remove them.
5. Practice and Practice. You will soon start figuring out the equation and there symmetry to resolve them fast.
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Some Important Books for Competitive Exam:
Detailed Trigonometry all formula pdf download Download
NCERT Trigonometry book pdf download download
Frequently Asked Questions(FAQ):
Q1: What formulas should I study for the SSC CHSL?
Ans: For SSC CHSL, you should study trigonometry formulas either from your Class 10 textbook or from this article.
Q2: What are the basic trigonometric ratios?
Ans: Sine, Cosine, Tangent, Cotangent, Secant and Cosecant.
Q3: What are all the formulas of trigonometry?
Ans: You can learn all the trigonometry formulas from this article. You will get to know about:
Q4: What are formulas for trigonometry ratios?
Ans: Sin A = Perpendicular/Hypotenuse Cos A = Base/Hypotenuse Tan A = Perpendicular/Base
Q5: How do I memorize maths trigonometry formulas?
Ans: Our academic experts advise you not to memorize these trigonometry formulas. The more you try to learn consciously, the more is the chance that you are going to forget it. The best way to learn these formulas is to write them on a piece of paper and refer to them while you solve the questions. This way you will be able to easily learn the Trigonometry formulas.
Q6: What are the three main functions in trigonometry?
Ans: Sin, Cos and Tan are three main function in trigonometry.
Q7: Can I get a trigonometry formulas list?
Ans: Yes, with the help of this article, you can get all the important trigonometry formulas in one place.
Q8: What are the fundamental trigonometry identities?
Ans: The three fundamental identities are: 1. sin^2 A + cos^2 A = 1 2. 1+tan^2 A = sec^2 A 3. 1+cot^2 A = csc^2 A
Q9: Trigonometry formulas are applicable to which triangle?
Ans: Rightangled triangle
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