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t formulae
Fp1 chapter 5 - the t-formulae
Term | Definition |
---|---|
when t = tan(theta/2), sin(theta) | 2t/(1+t^2) |
when t = tan(theta/2), cos(theta) | (1-t^2)/(1+t^2) |
when t = tan(theta/2), tan(theta) | 2t/(1-t^2) |
sine double angle formula | sin(2*theta) = 2cos(theta)sin(theta) |
secant relationship with cosine | sec(theta) = 1/cos(theta) |
cosine double angle formula | cos(2*theta) = cos^2(theta) - sin^2(theta) |
cosecant relationship with sine | cosec(theta) = 1/sin(theta) |
tangent double angle formula | tan(2*theta) = 2tan(theta)/(1-tan^2(theta)) |
cotangent relation with tangent | cot(theta) := tan(90-theta), cot(theta) = 1/tan(theta) |
differentiation of trig (yr 2) | d/dx (sin(kx)) -> kcos(kx) d/dx (cos(kx)) -> -ksin(kx) d/dx (tan(kx)) -> ksec^2(kx) d/dx (sec(kx)) -> ksec(kx)tan(kx) d/dx (cosec(kx)) -> -cosec(kx)cot(kx) d/dx (cot(kx)) -> -kcosec^2(kx) |
when t = tan(theta/2), sin(theta) | 2t/(1+t^2) |
when t = tan(theta/2), cos(theta) | (1-t^2)/(1+t^2) |
when t = tan(theta/2), tan(theta) | 2t/(1-t^2) |
sine double angle formula | sin(2*theta) = 2cos(theta)sin(theta) |
secant relationship with cosine | sec(theta) = 1/cos(theta) |
cosine double angle formula | cos(2*theta) = cos^2(theta) - sin^2(theta) |
cosecant relationship with sine | cosec(theta) = 1/sin(theta) |
tangent double angle formula | tan(2*theta) = 2tan(theta)/(1-tan^2(theta)) |
cotangent relation with tangent | cot(theta) := tan(90-theta), cot(theta) = 1/tan(theta) |
differentiation of trig (yr 2) | d/dx (sin(kx)) -> kcos(kx) d/dx (cos(kx)) -> -ksin(kx) d/dx (tan(kx)) -> ksec^2(kx) d/dx (sec(kx)) -> ksec(kx)tan(kx) d/dx (cosec(kx)) -> -cosec(kx)cot(kx) d/dx (cot(kx)) -> -kcosec^2(kx) |