1.1 KiB
| cards-deck |
|---|
| default_obsidian |
#math/calculus
#math/calculus
trig identity
basic
sin^2x ::: sin^2x+cos^2x=1 ^1651675101678
sin^2x halves ::: sin^2x=1/2(1-cos{2x}) ^1651675101686
cos^2x ::: \cos^2x=1/2(1+\cos{2x}) ^1651674952732
\sin x\cos x ::: =\frac{1}{2}sin2x ^1651675101693
tan^{2}x + 1
#card/reverse $tan^{2}x + 1 = sec^{2}x$ because: $\frac{sin^{2}x}{cos^{2}x} + \frac{cos^{2}x}{cos^{2}x} = \frac{1}{cos^{2}x}$ ^1651675939328
derivatives
\frac{dx}{dy}\sec x ::: \tan x \sec x ^1651677169665
\frac{dx}{dy}\tan x ::: \sec^{2}x ^1651679351621
\frac{d x}{d y} \ln |x| ::: \frac{1}{x} ^1652457023180
integrals
\int \sec x dx ::: \ln |\sec x + \tan x| ^1651679351627
\int \tan x dx ::: \ln |\cos x|+C ^1652457023184
crazy identities
\sin A \cos B ::: \frac{1}{2}(\sin(A-B)+\sin(A+B)) ^1651679351632
\sin A \sin B ::: \frac{1}{2}(\cos(A-B)-\cos(A+B)) ^1651679351636
\cos A \cos B ::: \frac{1}{2}(\cos(A-B)+\cos(A+B)) ^1651679351639
\csc^{2}x= ::: =1+\cot^{2}x ^1652457023188