Trigonometry

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The three basic trigonometric ratios are: 1. sine θ = opposite side/hypotenuse 2. cosine θ = adjacent side/hypotenuse 3. tangent θ = opposite side/adjacent side

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Cosecant θ is the reciprocal of sine θ. cosec θ = 1/sin θ = hypotenuse/opposite side Note: cosec θ × sin θ = 1

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Secant θ is the reciprocal of cosine θ. sec θ = 1/cos θ = hypotenuse/adjacent side Note: sec θ × cos θ = 1

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Cotangent θ is the reciprocal of tangent θ. cot θ = 1/tan θ = adjacent side/opposite side = cos θ/sin θ Note: cot θ × tan θ = 1

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sin² θ + cos² θ = 1 This is the most fundamental identity in trigonometry. It is derived from the Pythagorean theorem in a right triangle.

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1 + tan² θ = sec² θ This identity is derived by dividing the fundamental identity sin² θ + cos² θ = 1 by cos² θ.

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1 + cot² θ = cosec² θ This identity is derived by dividing the fundamental identity sin² θ + cos² θ = 1 by sin² θ.

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sin 30° = 1/2 cos 30° = √3/2 tan 30° = 1/√3