Class 10 Mathematics

Class 10th mathematics 

Topic :- Trigonometry 

 class 10 trigonometry provides the foundational knowledge of trigonometric ratios and identities, preparing students for more advanced concepts in higher classes and their applications in various fields. Trigonometry is a branch of mathematics that focuses on relationships between the sides and angles of triangles. The word trigonometry comes from the Latin derivative of Greek words for triangle (trigonon) and measure (metron). To learn trigonometry for Class 10, focus on understanding the basic trigonometric ratios (sine, cosine, tangent) and their relationships within a right-angled triangle. Mastering the trigonometric table and fundamental identities is crucial, alongside practice with various problem-solving techniques. In Class 10 trigonometry, understanding trigonometric ratios, their values for standard angles, and identities are crucial. The core concepts revolve around sine, cosine, and tangent ratios in right-angled triangles, along with their reciprocals (cosecant, secant, and cotangent). Standard angles like 0°, 30°, 45°, 60°, and 90° have specific trigonometric values that need to be memorized. Additionally, trigonometric identities like sin²θ + cos²θ = 1, along with complementary angle relationships, are important for problem-solving. 

Here's a more detailed breakdown:

1. Trigonometric Ratios:

Sine (sin θ): Opposite side / Hypotenuse

Cosine (cos θ): Adjacent side / Hypotenuse

Tangent (tan θ): Opposite side / Adjacent side

Cosecant (csc θ): 1 / sin θ or Hypotenuse / Opposite side

Secant (sec θ): 1 / cos θ or Hypotenuse / Adjacent side

Cotangent (cot θ): 1 / tan θ or Adjacent side / Opposite side 

2. Standard Angles:

0°, 30°, 45°, 60°, and 90°: are the key angles for which you need to know the trigonometric ratios.

These values are often presented in a table and should be memorized, according to Cuemath. 

3. Trigonometric Identities:

Pythagorean Identity: sin²θ + cos²θ = 1 

Other Identities: sec²θ - tan²θ = 1, and csc²θ - cot²θ = 1 

Complementary Angles: sin (90° - θ) = cos θ, cos (90° - θ) = sin θ, and so on 

4. Applications:

Trigonometry is used in various fields like engineering, physics, and architecture to solve problems related to heights, distances, and angles.

Specifically, in Class 10, you'll encounter applications like calculating the height of a building or the angle of elevation/depression. 

5. Complementary Angles:

If the sum of two angles is 90°, they are called complementary angles. 

Understanding the relationships between trigonometric ratios of complementary angles is important for solving problems.