கணிதம் உங்களுக்காக - 3 - கான்ஸெப்ட்கள்

 9. 45°-45°-90° triangle: The legs are congruent, and the hypotenuse is √2 times the length of each leg.

10. 30°-60°-90° triangle: The length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

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

12. Arc length of a sector: L = rθ

13. Area of a segment: A = ½r²(θ - sinθ)

14. Volume of a cone: V = ⅓πr²h

15. Surface area of a cone: SA = πr(r + √(r² + h²))

16. Volume of a pyramid: V = ⅓Bh (where B is the area of the base and h is the height)

17. Surface area of a pyramid: SA = B + ½Pl (where B is the area of the base, P is the perimeter of the base, and l is the slant height)

18. Volume of a prism: V = Bh (where B is the area of the base and h is the height)

19. Surface area of a prism: SA = 2B + Ph (where B is the area of the base and P is the perimeter of the base)

20. Volume of a hemisphere: V = ⅔πr³

21. Surface area of a hemisphere: SA = 3πr²

1. Sine: sin(θ) = opposite / hypotenuse

2. Cosine: cos(θ) = adjacent / hypotenuse

3. Tangent: tan(θ) = opposite / adjacent

4. Pythagorean Identity: sin²(θ) + cos²(θ) = 1

5. Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)

6. Cosine Rule: c² = a² + b² - 2ab cos(C)

7. Area of a triangle: A = ½ab sin(C)

8. Distance between two points: d = √((x₂ - x₁)² + (y₂ - y₁)²)

9. Midpoint of a line segment: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

10. Slope of a line: m = (y₂ - y₁) / (x₂ - x₁)

11. Equation of a line: y = mx + c

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

13. Reflection over the x-axis: (x, y) → (x, -y)

14. Reflection over the y-axis: (x, y) → (-x, y)

15. Reflection over the line y = x: (x, y) → (y, x)

16. Rotation by θ degrees: (x', y') = (x cos(θ) - y sin(θ), x sin(θ) + y cos(θ))

17. Translation: (x, y) → (x + a, y + b)

18. Volume of a tetrahedron: V = (1/6) × |a · (b × c)| (where a, b, and c are vectors representing the edges meeting at one vertex)

19. Surface area of a tetrahedron: SA = a²√3 (for a regular tetrahedron with edge length a)

20. Volume of a prism: V = Bh (where B is the area of the base and h is the height)

21. Surface area of a prism: SA = 2B + Ph (where B is the area of the base and P is the perimeter of the base)

22. Volume of a torus: V = 2π²Rr² (where R is the distance from the center of the tube to the center of the torus and r is the radius of the tube)

23. Surface area of a torus: SA = 4π²Rr

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