Trigonometric Identities Involving Sine And Cosine
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Trigonometric identities involving sine and cosine The fundamental identity cos2(θ)+sin2(θ) = 1 Symmetry identities cos(–θ) = cos(θ) sin(–θ) = –sin(θ) cos(π+θ) = –cos(θ) sin(π+θ) = –sin(θ) cos(π–θ) = –cos(θ) sin(π–θ) = sin(θ) cos(π/2 + θ) = –sin(θ) sin(π/2 + θ) = cos(θ) cos(π/2 – θ) = sin(θ) sin(π/2 – θ) = cos(θ) Addition formulas cos(α+β) = cos(α)cos(β)–sin(α)sin(β) cos(α–β) = cos(α)cos(β)+sin(α)sin(β) sin(α+β) = sin(α)cos(β)+cos(α)sin(β) sin(α–β) = sin(α)cos(β)–cos(α)sin(β) Double-angle formulas cos(2θ) = cos2(θ)–sin2(θ) = 1–2sin2(θ) = 2cos2(θ)–1 sin(2θ) = 2sin(θ)cos(θ) Sum and difference formulas cos(α)+cos(β) = 2cos(½(α+β))cos(½(α–β)) cos(α)–cos(β) = 2sin(½(α+β))sin(½(β–α)) sin(α)+sin(β) = 2sin(½(α+β))cos(½(α–β)) sin(α)–sin(β) = 2cos(½(α+β))sin(½(α–β)) Product formulas cos(α)cos(β) = ½(cos(α–β)+cos(α+β)) sin(α)sin(β) = ½(cos(α–β)–cos(α+β)) sin(α)cos(β) = ½(sin(α–β)+sin(α+β))
Tag » What Is Sin Pi 2
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