**Trigonometry Formulas Pdf: Chart, Table, Sheet and Functions**: I welcome all of you in this new post. If you are looking for Trigonometry Table, then you will get it from here.

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## Trigonometry Table 2023

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## Trigonometry Formula Pdf

- Changes Between Angles
- Some Important Facts
- If (x+y) = 90*
- If (A+B+C) = 180*
- Maximum & Minimum Values
- Trigonometric Values

There are lots to learn in Trigonometry. And after your concept on Trigonometric Functions becomes clear, then you will be able to score good marks in this chapter. It becomes very easy for you after you understand its concept properly.

This is the normal table of trigonometric formulas, now you can also check out the other advanced formulas of Trigonometry.

## Trigonometry Functions

Below you can check the Reciprocal identities given and these are also most important part of trigonometric formulas.

- 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

**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 Angle Identities**

- sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan
^{2}x)] - cos(2x) = cos
^{2}(x)–sin^{2}(x) = [(1-tan^{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/(2-sec^{2}x) - csc (2x) = (sec x. csc x)/2

**Triple Angle Identities**

- Sin 3x = 3sin x – 4sin
^{3}x - Cos 3x = 4cos
^{3}x-3cos x - Tan 3x = [3tanx-tan
^{3}x]/[1-3tan^{2}x]

**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

**Cofunction Identities (in Degrees)**

The cofunction or periodic identities can also be represented in degrees as:

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

Trigonometry Formulas Pdf download

Trigonometry: Exploring the Depths of Triangles and Beyond

Trigonometry, derived from the Greek words “trigonon” (meaning triangle) and “metron” (meaning measure), is a branch of mathematics that delves into the study of relationships between angles and sides of triangles. It serves as a fundamental pillar in mathematics and finds extensive applications in various fields, ranging from physics and engineering to architecture and navigation. In this article, we will explore the key components of trigonometry, including trigonometric functions, ratios, identities, equations, graphs, and their practical applications.

Trigonometric Functions: Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are defined based on the ratios of the sides of a right triangle, such as opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent. Trigonometric functions form the foundation of trigonometry, enabling us to analyze and solve a wide range of problems involving angles and triangles.

Trigonometric Ratios: Trigonometric ratios are specific relationships between the sides of a right triangle and the angles within it. The three primary trigonometric ratios are sine, cosine, and tangent. Sine (sin) is the ratio of the length of the side opposite an angle to the hypotenuse, cosine (cos) is the ratio of the length of the side adjacent to an angle to the hypotenuse, and tangent (tan) is the ratio of the length of the side opposite an angle to the side adjacent to it. These ratios enable us to determine unknown side lengths or angles within a triangle.

Trigonometric Identities: Trigonometric identities are equations that are true for all values of the variables involved. They establish connections and relationships between trigonometric functions. Some of the fundamental trigonometric identities include the Pythagorean identities, reciprocal identities, quotient identities, and the even-odd identities. These identities serve as powerful tools for simplifying trigonometric expressions, proving trigonometric equations, and solving complex trigonometric problems.

Trigonometric Equations: Trigonometric equations involve trigonometric functions and unknown variables. Solving these equations entails finding the values of the variables that satisfy the given equation. Trigonometric equations can be solved algebraically or graphically, using various methods such as factoring, substitution, or applying trigonometric identities. These equations find applications in diverse fields, such as physics, engineering, and astronomy, where precise calculations and predictions are required.

Trigonometric Graphs: Trigonometric graphs depict the relationships between angles and the values of trigonometric functions. The graphs exhibit periodic patterns due to the periodic nature of trigonometric functions. Sine and cosine functions generate sinusoidal waves, whereas tangent functions produce asymptotic lines with vertical asymptotes. Trigonometric graphs enable us to visualize the behavior and characteristics of trigonometric functions, facilitating a deeper understanding of their properties and applications.

Trigonometric Applications: Trigonometry finds widespread applications in numerous fields. In physics, trigonometry helps analyze the motion of objects, waveforms, and oscillations. Engineers employ trigonometry to design structures, calculate forces, and model electrical systems. Architects rely on trigonometry to ensure accurate measurements and angles in building designs. Navigators and astronomers use trigonometry to determine positions, distances, and angles of celestial objects. Additionally, trigonometry plays a vital role in computer graphics, sound engineering, and the study of periodic phenomena.

In conclusion, trigonometry is a versatile branch of mathematics that investigates the intricate relationships between angles and sides of triangles. Trigonometric functions, ratios, identities, equations, and graphs form the building blocks of this discipline. By employing trigonometry, mathematicians, scientists, engineers, and professionals in various fields unlock the means to solve complex problems, make accurate predictions, and understand the world around us. Trigonometry’s indispensable applications have solidified its place as a cornerstone of mathematical knowledge, enabling us to explore and comprehend the depths of triangles and beyond.

**Conclusion**: If you liked all the above mentioned formulas of Trigonometry and also trigonometry table, then share this post with your friends.

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