கணிதம் உங்களுக்காக - 5 - கான்ஸெப்ட்கள்

1. Exterior angle of a regular polygon: Exterior angle = 360° / n (where n is the number of sides)

2. Interior angle of a regular polygon: Interior angle = 180° - Exterior angle

3. Area of a regular polygon: A = (1/4)ns²cot(π/n) (where n is the number of sides and s is the side length)

4. Sum of interior angles of a polygon: Sum = (n-2) × 180° (where n is the number of sides)

5. Surface area of a rectangular prism: SA = 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height)

6. Volume of a triangular prism: V = (1/2)bhL (where b is the base length, h is the height, and L is the length of the prism)

7. Surface area of a triangular prism: SA = bh + 2ls + lb (where b is the base length, h is the height, l is the length, and s is the slant height)

8. Volume of an elliptical cylinder: V = πabH (where a and b are the semi-major and semi-minor axes of the elliptical base, and H is the height)

9. Surface area of an elliptical cylinder: SA = 2πa² + 2πaH + 2πbH

10. Distance between two points in space: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

11. Equation of a sphere: (x - h)² + (y - k)² + (z - l)² = r² (where (h, k, l) is the center and r is the radius)

12. Volume of a frustum: V = (1/3)πh(R₁² + R₁R₂ + R₂²) (where h is the height, R₁ is the radius of the top base, and R₂ is the radius of the bottom base)

13. Surface area of a frustum: SA = π(R₁ + R₂)√((R₂ - R₁)² + h²) + πR₁² + πR₂²

14. Heron's Formula for the area of a triangle: A = √(s(s - a)(s - b)(s - c)) (where s = (a + b + c)/2 and a, b, and c are the lengths of the sides)

15. Law of Cotangents: (a + b + c)cot(A/2) = a cot(B/2) + b cot(C/2)

16. Product-to-Sum Formulas:

    - sin(A)sin(B) = 1/2[cos(A - B) - cos(A + B)]

    - cos(A)cos(B) = 1/2[cos(A + B) + cos(A - B)]

    - sin(A)cos(B) = 1/2[sin(A + B) + sin(A - B)]

17. Section formula (Internal Division): (x, y) = ((mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)) (where a point divides the line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n)

18. Section formula (External Division): (x, y) = ((mx₂ - nx₁) / (m - n), (my₂ - ny₁) / (m - n)) (where a point divides the line segment joining (x₁, y₁) and (x₂, y₂) externally in the ratio m:n)