# 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)
• 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 : 31 July, 2024

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