Term
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Definition
cos2(x)+sin2(x)=1
tan2(x)+1=sec2(x)
cot2(x)+1=csc2(x) |
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Term
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Definition
sin(s+t)=sin(s)cos(t)+cos(s)sin(t) cos(s+t)=cos(s)cos(t)-sin(s)sin(t) tan(s+t)=&fractan(s)+tan(t)1-tan(s)tan(t);
= sin(s+t)
cos(s+t)
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Term
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Definition
sin(s-t)=sin(s)cos(t)-cos(s)sin(t)
cos(s-t)=cos(s)cos(t)+sin(s)sin(t)
tan(s-t)=(tan(s)-tan(t))/(1+tan(s)tan(t))=(sin(s-t))/(cos(s-t)) |
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Term
| Double-angle formula for sine |
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Definition
| sin(2x)=sin(x+x)=sin(x)cos(x)+cos(x)sin(x)=2sin(x)cos(x) |
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Term
| Double angle formula for cosine |
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Definition
| cos(2x)=cos(x+x)=cos(x)cos(x)-sin(x)sin(x)=cos^2(x)-sin^2(x)=2cos^2(x)-1=1-2sin^2(x) |
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Term
| Double-angle formula for tangent |
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Definition
| tan(2x)=(sin(2x))/(cos(2x))=(2tan(x))/(1-tan^2(x)) |
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Term
| Lowering Degree Identity for cos^2(x) |
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Definition
cos(2x)=2cos^2(x)-1
=cos(2x)+1=2cos^2(x)
=(1+cos(2x))/2=cos^2(x) |
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Term
| Lowering Degree Identity for sin^2(x) |
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Definition
cos(2x)=1-2sin^2(x)
=cos(2x)-1=-2sin^2(x)
=(cos(2x)-1)/-2=sin^2(x)
=(1-cos(2x))/2=sin^2(x) |
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Term
| Lowering Degree Identity for tan^2(x) |
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Definition
| (1-cos(2x))/(1+cos(2x))=tan^2(x) |
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Term
| Half-angle formula for cosine |
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Definition
cos^2(x/2)=(cos(2(x/2)+1))/2
=(cos(x)+1)/2
cos(x/2)= +or- sqrt((cos(x)+1)/2) |
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Term
| Half-angle formula for sine |
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Definition
sin(x/2)= +or- sqrt((1-cos(x))/2)
or
sin^(2)(x)=(1/2)(1-cos(2x)) |
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Term
| Half-angle formula for tangent |
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Definition
| tan(x/2)=(1-cos(x))/(sin(x))=(sin(x))/(1+cos(x)) |
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