Trigonometric Ratios

Trigonometric Ratios

• Sine (sin): The ratio of the opposite side to the hypotenuse in a right-angled triangle.
  • sin(A) = opposite side / hypotenuse
• Cosine (cos): The ratio of the adjacent side to the hypotenuse in a right-angled triangle.
  • cos(A) = adjacent side / hypotenuse
• Tangent (tan): The ratio of the opposite side to the adjacent side in a right-angled triangle.
  • tan(A) = opposite side / adjacent side
• Cotangent (cot): The ratio of the adjacent side to the opposite side in a right-angled triangle.
  • cot(A) = adjacent side / opposite side
• Secant (sec): The ratio of the hypotenuse to the adjacent side in a right-angled triangle.
  • sec(A) = hypotenuse / adjacent side
• Cosecant (csc): The ratio of the hypotenuse to the opposite side in a right-angled triangle.
  • csc(A) = hypotenuse / opposite side

Trigonometric Identities

• Pythagorean Identity:
  • sin^2(A) + cos^2(A) = 1
• Sum and Difference Formulas:
  • sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
  • cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
  • tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
• Double Angle Formulas:
  • sin(2A) = 2sin(A)cos(A)
  • cos(2A) = cos^2(A) - sin^2(A)
• Half Angle Formulas:
  • sin(A/2) = ±√((1 - cos(A)) / 2)
  • cos(A/2) = ±√((1 + cos(A)) / 2)

Trigonometric Ratios

• Sine (sin): Ratio of the opposite side to the hypotenuse in a right-angled triangle.
• Cosine (cos): Ratio of the adjacent side to the hypotenuse in a right-angled triangle.
• Tangent (tan): Ratio of the opposite side to the adjacent side in a right-angled triangle.
• Cotangent (cot): Ratio of the adjacent side to the opposite side in a right-angled triangle.
• Secant (sec): Ratio of the hypotenuse to the adjacent side in a right-angled triangle.
• Cosecant (csc): Ratio of the hypotenuse to the opposite side in a right-angled triangle.

Trigonometric Identities

• Pythagorean Identity: sin^2(A) + cos^2(A) = 1.
• Sum and Difference Formulas: used to find trigonometric values of sums and differences of angles.
  • sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
  • cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
  • tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
• Double Angle Formulas: used to find trigonometric values of double angles.
  • sin(2A) = 2sin(A)cos(A)
  • cos(2A) = cos^2(A) - sin^2(A)
• Half Angle Formulas: used to find trigonometric values of half angles.
  • sin(A/2) = ±√((1 - cos(A)) / 2)
  • cos(A/2) = ±√((1 + cos(A)) / 2)

Learn about sine, cosine, tangent, and cotangent ratios in right-angled triangles, including their definitions and formulas.