கணிதம் உங்களுக்காக - 9 - கான்ஸெப்ட்கள்

 1. Volume of a truncated cone (frustum of a cone): 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)

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

3. Volume of a spherical cap: V = (1/3)πh²(3R - h) (where h is the height of the cap and R is the radius of the sphere)

4. Surface area of a spherical cap: SA = 2πRh (where h is the height of the cap and R is the radius of the sphere)

5. Volume of a spherical sector: V = (2/3)πR²h (where R is the radius of the sphere and h is the height of the spherical sector)

6. Volume of a spherical segment: V = (1/6)πh(3a² + 3b² + h²) (where h is the height of the segment, a and b are the radii of the segment's bases)

7. Triple Angle Formulas:

    - sin(3A) = 3 sinA - 4 sin³A

    - cos(3A) = 4 cos³A - 3 cosA

    - tan(3A) = (3 tanA - tan³A) / (1 - 3 tan²A)

8. Product-to-Sum Formulas:

    - sin(A) sin(B) = ½ [cos(A - B) - cos(A + B)]

    - cos(A) cos(B) = ½ [cos(A + B) + cos(A - B)]

    - sin(A) cos(B) = ½ [sin(A + B) + sin(A - B)]

9. Power of a Point Theorem:

    - If a point P lies outside a circle and two secant lines PA and PB intersect the circle at A and B, then PA × PB = PC × PD (where C and D are points of intersection)

10. Segment lengths in a circle: If two chords AB and CD intersect at point P inside the circle, then PA × PB = PC × PD.

11. Length of a tangent segment: If a tangent from an external point P touches the circle at T, then PT² = PA × PB (where A and B are points of intersection of a secant through P)

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

13. General form of the equation of a circle: (x - h)² + (y - k)² = r² (where (h, k) is the center and r is the radius)

14. Equation of a parabola: y = ax² + bx + c or (y - k) = a(x - h)² (where (h, k) is the vertex)

15. Equation of an ellipse: (x - h)²/a² + (y - k)²/b² = 1 (where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis)

16. Equation of a hyperbola: (x - h)²/a² - (y - k)²/b² = 1 (horizontal) or (y - k)²/a² - (x - h)²/b² = 1 (vertical)

17. Sum of exterior angles of a polygon: 360°

18. Diagonals of a polygon: n(n - 3) / 2 (where n is the number of sides)

19. Interior angle of a regular polygon: (n - 2) × 180° / n (where n is the number of sides)

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

21. Area of a regular polygon: A = ½ × Perimeter × Apothem (where Perimeter = n × s, n is the number of sides, s is the side length, and the Apothem is the perpendicular distance from the center to a side)