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Trigonometric Identities & Formulas

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Law of Cosines

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c2=a2+b22abcos(C)c^2 = a^2 + b^2 - 2ab\cos(C)

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Pythagorean Identity

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sin2(θ)+cos2(θ)=1\sin^2(θ) + \cos^2(θ) = 1

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Double Angle Formula for Cosine

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cos(2θ)=cos2(θ)sin2(θ)\cos(2θ) = \cos^2(θ) - \sin^2(θ)

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Law of Sines

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sin(A)a=sin(B)b=sin(C)c\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}

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Tangent of Sum

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tan(α+β)=tan(α)+tan(β)1tan(α)tan(β)\tan(α + β) = \frac{\tan(α) + \tan(β)}{1 - \tan(α)\tan(β)}

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Sum of Angles for Cosine

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cos(α+β)=cos(α)cos(β)sin(α)sin(β)\cos(α + β) = \cos(α)\cos(β) - \sin(α)\sin(β)

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Sum of Angles for Sine

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sin(α+β)=sin(α)cos(β)+cos(α)sin(β)\sin(α + β) = \sin(α)\cos(β) + \cos(α)\sin(β)

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Double Angle Formula for Sine

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sin(2θ)=2sin(θ)cos(θ)\sin(2θ) = 2\sin(θ)\cos(θ)

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