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Math 1275/D500 Instructor: Suman Ganguli Fundamental Trigonometric Identities tan θ = sin θ cos θ cot θ = 1 cos θ = tan θ sin θ csc θ = 1 sin θ sec θ = 1 cos θ sin2 θ + cos2 θ = 1 =⇒ sin2 θ = 1 − cos2 θ& cos2 θ = 1 − sin2 θ tan2 θ + 1 = sec2 θ cot2 θ + 1 = csc2 θ Law of Sines & Law of Cosines For any triangle (i.e., not necessarily a right triangle) with sidelengths a, b, c and corresponding angles A, B, C (as shown): Law of Sines: sin A a = sin B sin C = b c Law of Cosines: a2 = b2 + c2 − 2bc cos A b2 = a2 + c2 − 2ac cos B 2 = a2 + b2 − 2ab cos C c