Trigonometry in Mathematics (Maths) Class 10

Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is an important topic in Class 10 mathematics and is used in various fields such as engineering, physics, and astronomy. Here is a detailed explanation of trigonometry in Class 10:

Basics of Trigonometry
- Trigonometry is based on six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent.
- These ratios are defined as the ratios of the sides of a right-angled triangle.

Trigonometric Ratios
- Sine (sinθ) = Opposite side / Hypotenuse
- Cosine (cosθ) = Adjacent side / Hypotenuse
- Tangent (tanθ) = Opposite side / Adjacent side
- Cosecant (cosecθ) = 1 / sinθ
- Secant (secθ) = 1 / cosθ
- Cotangent (cotθ) = 1 / tanθ

Applications of Trigonometry
- Trigonometry is used to solve problems involving angles and distances.
- It is used in navigation, surveying, and construction.
- Trigonometric functions are used to model periodic phenomena such as sound waves and light waves.

Trigonometric Identities
- Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ
- Cofunction identities: sin(π/2 - θ) = cosθ, tan(π/2 - θ) = cotθ, sec(π/2 - θ) = cscθ

Trigonometry Formulas
- Law of Sines: a/sinA = b/sinB = c/sinC
- Law of Cosines: a² = b² + c² - 2bc cosA

Trigonometry is a fundamental topic in mathematics that lays the foundation for understanding more advanced concepts in geometry and calculus. It is essential for students to grasp the concepts of trigonometry to excel in their academic pursuits.