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8 Cards in this Set
- Front
- Back
- 3rd side (hint)
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QUOTIENT IDENTITIES
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tanθ=sinθ/cosθ
cotθ=cosθ/sinθ |
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RECIPROCAL IDENTITIES
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sinθ=1/cscθ
cosθ=1/secθ tanθ=1/cotθ cscθ=1/sinθ secθ=1/cosθ cotθ=1/tan |
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PYTHAGOREAN IDENTITIES
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sin(^2)θ+cos(^2)θ=1
1+cot(^2)θ=csc(^2)θ tan(^2)θ+1=sec(^2)θ |
so if you just have sin squared or cos squared, you can move the other term to the opposite side (sine squared equals 1 minus cosine squared); this goes for the other pythagorean identities as well
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EVEN/ODD IDENTITIES
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sin(-θ)=-sinθ
tan(-θ)=-tanθ csc(-θ)=-cscθ cot(-θ)=-cotθ cos(-θ)=cosθ sec(-θ)=secθ |
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SUM/DIFFERENCE IDENTITIES
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cos(α+β)=cos(α)cos(β)-sin(α)sin(β)
cos(α-B)=cos(α)cos(β)+sin(α)sin(β) sin(α±β)=sin(α)cos(β)±cos(α)sin(β) tan(α+β)=tan(α)+tan(β)/ 1-tan(α)tan(β) tan(α-β)=tan(α)-tan(β)/ 1+tan(α)tan(β) |
sin=y/r
cos=x/r tan=y/x cot=1/tan sec=1/cos csc=1/sin |
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DOUBLE ANGLES
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sin(2θ)=2sinθcosθ
cos(2θ)=cos(^2)θ-sin(^2)θ cos(2θ)=2cos(^2)θ-1 cos(2θ)=1-2sin(^2)θ tan(2θ)=2tanθ/1-tan(^2)θ |
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HALF ANGLES
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sin(^2)(α/2)=(1-cosα)/2
sin(α/2)=±√((1-cosα)/2) cos(α/2)=±√((1-cosα)/2) tan(^2)(α/2)=(1-cosα)/(1+cosα) tan(α/2)=±√((1-cosα)/(1+cosα)) |
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SPECIAL FORMULAS
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sin(^2)θ=(1-cos(2θ))/2
cos(^2)θ=(cos(2θ)+1)/2 tan(^2)θ=(1-cos(2θ))/(1+cos(2θ)) cos((π/2)-θ)=sinθ sin((π/2)-θ)=cosθ |
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