# Trigonometry: Trigonometric Functions and Identities

HappierDallas
·
·

Start Quiz

Study Flashcards

## 5 Questions

### किस तत्व में कहा गया है कि sin(π - A) = -sin(A) और cos(π - A) = -cos(A) ?

अद्वितीय और विषम गुण

### किस तत्व को 'पैथागोरियन तत्व' कहा जाता है?

sin²(A) + cos²(A) = 1

-cot(A)

संयोजन सूत्र

संक्षेपन सूत्र

## Trigonometry: Understanding Functions and Identities

Trigonometry is a fundamental branch of mathematics that focuses on the relationships between the sides and angles of triangles. Two crucial aspects of trigonometry are trigonometric functions and trigonometric identities. In this article, we will explore both topics in detail.

### Trigonometric Functions

There are six basic trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions are defined relative to the sides and angles of a right triangle.

• Sine (sin): The ratio of the side opposite an angle to the length of the hypotenuse, i.e., sin A = opposite side / hypotenuse.
• Cosine (cos): The ratio of the adjacent side to the length of the hypotenuse, i.e., cos A = adjacent side / hypotenuse.
• Tangent (tan): The ratio of the side opposite an angle to the adjacent side, i.e., tan A = opposite side / adjacent side.
• Cotangent (cot): The reciprocal of the tangent function, i.e., cot A = adjacent side / opposite side.
• Secant (sec): The reciprocal of the cosine function, i.e., sec A = hypotenuse / adjacent side.
• Cosecant (csc): The reciprocal of the sine function, i.e., csc A = hypotenuse / opposite side.

These functions are essential tools in solving problems related to the angles and sides of triangles, such as calculating unknown angles and distances.

### Trigonometric Identities

Trigonometric identities are mathematical statements that relate the values of different trigonometric functions for the same angle. Some common trigonometric identities include:

• Pythagorean Identity: sin²(A) + cos²(A) = 1 for any angle A.
• Reciprocal Identities: sin(-A) = -sin(A), cos(-A) = cos(A), tan(-A) = -tan(A), cot(-A) = -cot(A), sec(-A) = -csc(A), and csc(-A) = -sec(A).
• Even and Odd Properties: sin(π - A) = -sin(A) and cos(π - A) = -cos(A) for any angle A.
• Addition Formulae: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), cos(A + B) = cos(A)cos(B) - sin(A)sin(B), tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)), cot(A + B) = (cot(A) + cot(B)) / (1 + cot(A)cot(B)), sec(A + B) = sec(A)sec(B) / |cos(A + B)|, and csc(A + B) = csc(A)csc(B) / |sin(A + B)|.
• Subtraction Formulae: sin(A - B) = sin(A)cos(B) - cos(A)sin(B), cos(A - B) = cos(A)cos(B) + sin(A)sin(B), tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B)), cot(A - B) = (cot(A) - cot(B)) / (1 - cot(A)cot(B)), sec(A - B) = sec(A)sec(B) / |cos(A - B)|, and csc(A - B) = csc(A)csc(B) / |sin(A - B)|.

These identities are used to simplify trigonometric expressions and equations, making calculations easier.

ट्राइगनॉमेट्री एक मौलिक गणित की शाखा है जो त्रिभुज के कोनों और भुजों के बीच संबंधों पर ध्यान केंद्रित करती है। इस लेख में, हम त्रिकोणमितीय कार्यों और त्रिकोणमितीय पहचानों के दो महत्वपूर्ण पहलुओं की विस्तार से जांच करेंगे।

## Make Your Own Quizzes and Flashcards

Convert your notes into interactive study material.

## More Quizzes Like This

12 questions
11 questions
5 questions
Use Quizgecko on...
Browser
Information:
Success:
Error: