Trigonometric Ratios

Trigonometric Ratio Abbreviation Definition Reciprocal Ratio Reciprocal Abbreviation
Sine sin(θ) Opposite/Hypotenuse Cosecant csc(θ) = 1/sin(θ)
Cosine cos(θ) Adjacent/Hypotenuse Secant sec(θ) = 1/cos(θ)
Tangent tan(θ) Opposite/Adjacent Cotangent cot(θ) = 1/tan(θ)
Cosecant csc(θ) 1/sin(θ) Sine sin(θ) = 1/csc(θ)
Secant sec(θ) 1/cos(θ) Cosine cos(θ) = 1/sec(θ)
Cotangent cot(θ) 1/tan(θ) Tangent tan(θ) = 1/cot(θ)
Additional Properties
  • Pythagorean Identity:
    • sin²(θ) + cos²(θ) = 1
    • sec²(θ) - tan²(θ) = 1
    • csc²(θ) - cot²(θ) = 1
  • Reciprocal Identities:
    • sin(θ) = 1/csc(θ)
    • cos(θ) = 1/sec(θ)
    • tan(θ) = 1/cot(θ)
  • Quotient Identities:
    • tan(θ) = sin(θ) / cos(θ)
    • cot(θ) = cos(θ) / sin(θ)
  • Even-Odd Identities:
    • sin(-θ) = -sin(θ)
    • cos(-θ) = cos(θ)
    • tan(-θ) = -tan(θ)
  • Cofunction Identities:
    • sin(90° - θ) = cos(θ)
    • cos(90° - θ) = sin(θ)
    • tan(90° - θ) = 1/tan(θ)

Last Updated : 03 October, 2024

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