Trigonometric Ratios
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Questions and Answers

What is the value of sin^2(A) + cos^2(A) in a right-angled triangle?

  • 2
  • sin(A) + cos(A)
  • 0
  • 1 (correct)

    • What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?

  • tangent
  • cosine
  • cotangent
  • sine (correct)

    • What is the formula for sin(A + B) in a right-angled triangle?

  • sin(A)cos(B) - cos(A)sin(B)
  • sin(A) - sin(B)
  • sin(A)cos(B) + cos(A)sin(B) (correct)
  • sin(A) + sin(B)

    • What is the formula for cos(2A) in a right-angled triangle?

    <p>cos^2(A) - sin^2(A)</p> Signup and view all the answers

    What is the formula for tan(A + B) in a right-angled triangle?

    <p>(tan(A) + tan(B)) / (1 - tan(A)tan(B))</p> Signup and view all the answers

    What is the formula for sin(A/2) in a right-angled triangle?

    <p>±√((1 - cos(A)) / 2)</p> Signup and view all the answers

    What is the ratio of the adjacent side to the opposite side in a right-angled triangle?

    <p>cotangent</p> Signup and view all the answers

    What is the ratio of the hypotenuse to the opposite side in a right-angled triangle?

    <p>cosecant</p> Signup and view all the answers

    Study Notes

    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)

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    Description

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

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