கணிதம் உங்களுக்காக - 4 - கான்ஸெப்ட்கள்

 1. Standard form of a parabola (vertical): (x - h)² = 4p(y - k)

2. Standard form of a parabola (horizontal): (y - k)² = 4p(x - h)

3. Standard form of an ellipse: (x - h)²/a² + (y - k)²/b² = 1 (a > b)

4. Standard form of a hyperbola (horizontal): (x - h)²/a² - (y - k)²/b² = 1

5. Standard form of a hyperbola (vertical): (y - k)²/a² - (x - h)²/b² = 1

6. Equation of a circle: (x - h)² + (y - k)² = r²

7. Volume of a frustum: V = (1/3)πh(R² + Rr + r²)

8. Surface area of a frustum: SA = π(R + r)√((R - r)² + h²) + πR² + πr²

9. Dot product: A · B = |A||B|cos(θ)

10. Cross product: A × B = |A||B|sin(θ)n

11. Magnitude of a vector: |A| = √(A₁² + A₂² + A₃²)

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

13. Area of a regular n-sided polygon with side length s: A = (n × s²) / (4 × tan(π/n))

14. Surface area of a regular tetrahedron with side length a: SA = √3 × a²

15. Volume of an oblique cylinder: V = πr²h

16. Volume of an oblique cone: V = (1/3)πr²h

1. Area of a sector: A = ½r²θ (where r is the radius and θ is the central angle in radians)

2. Arc length: L = rθ

3. Length of a chord: c = 2r sin(θ/2) (where r is the radius and θ is the central angle in radians)

4. Segment area: A = ½r²(θ - sinθ)

5. Equation of a line in slope-intercept form: y = mx + c

6. Equation of a line in point-slope form: y - y₁ = m(x - x₁)

7. General form of a line equation: Ax + By + C = 0

8. Distance from a point to a line: d = |Ax₁ + By₁ + C| / √(A² + B²)

9. Equation of a plane: Ax + By + Cz + D = 0

10. Distance from a point to a plane: d = |Ax₁ + By₁ + Cz₁ + D| / √(A² + B² + C²)

11. Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

12. Law of Cosines: c² = a² + b² - 2ab cos(C)

13. Law of Tangents: (a - b) / (a + b) = tan[(A - B)/2] / tan[(A + B)/2]

14. Area of a triangle using trigonometry: A = ½ab sin(C)

15. Angle sum and difference identities:

    - sin(A ± B) = sinA cosB ± cosA sinB

    - cos(A ± B) = cosA cosB ∓ sinA sinB

    - tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)

16. Double angle formulas:

    - sin(2A) = 2 sinA cosA

    - cos(2A) = cos²A - sin²A = 2 cos²A - 1 = 1 - 2 sin²A

    - tan(2A) = 2 tanA / (1 - tan²A)

17. Projection of vector A onto vector B: proj_B(A) = (A · B / |B|²) B

18. Angle between two vectors: cos(θ) = (A · B) / (|A||B|)

19. Lateral surface area of a cone: SA_lateral = πr√(r² + h²)

20. Lateral surface area of a cylinder: SA_lateral = 2πrh

21. Total surface area of a cylinder: SA_total = 2πr(h + r)

22. Volume of a triangular prism: V = ½bhL (where b is the base length, h is the height, and L is the length of the prism)

23. Volume of a parallelepiped: V = |a · (b × c)| (where a, b, and c are vectors representing the edges)