modern periodic table

Learn table of Pythagorean related trigonometric identities:cos2θ + sin2θ = 1sin θ = ± `sqrt(1 - cos^2 theta)`cos θ = ± `sqrt(1 - sin^2 theta)`sin θ = `1/(csc theta)`cos θ = `1/(sec theta)` tan θ = `1/(cot theta)`csc   θ = `1/(sin theta)` sec   θ = `1/(cos theta)`  cot   θ = `1/(tan theta)`1 + tan2θ = sec2θ1 + cot2θ = csc2θsin θ = ± `(tan theta)/(sqrt(1 + tan^2theta))`cos θ = ± `1/(sqrt(1 + tan^2theta))`tan θ = Â± `sqrt(sec^2 theta - 1)`csc θ = ± `(sqrt(1 + tan^2theta))/(tan theta)`    sec θ = ± `(sqrt(1 + tan^2theta))`cot θ =  ± `1/(sqrt(sec^2 theta - 1))`Learn table of symmetry related trigonometric identities:sin (-θ) = - sin θ       cos (-θ) = + cos θ      tan (-θ) = - tan θ   csc (-θ) = - csc θ  sec (-θ) = + sec θ      cot (-θ) = - cot θ     sin (∏ - θ) = + sin θcos (∏ - θ) = - cos θtan (∏ - θ) = - tan θcsc (∏ - θ) = + csc θsec (∏ - θ) = - sec θcot (∏ - θ) = - cot sin (`pi/2` - θ) = + cos θcos (`pi/2` - θ) = + sin θtan (`pi/2` - θ) = + cot θcsc (`pi/2` - θ) = + sec θsec (`pi/2` - θ) = + csc θcot (`pi/2` - θ) = + tan θLearn table of shifts and periodicity related trigonometric identities:sin (θ + `pi/2` ) = + cos θ cos (θ + `pi/2` ) = - sin θ tan (θ + `pi/2` ) = - cot θ   csc (θ + `pi/2` ) = + sec θsec (θ + `pi/2` ) = - csc θ     cot (θ + `pi/2` ) = - tan θ    sin (θ + ∏) = - sin θcos (θ + ∏) = - cos θtan (θ + ∏) = + tan θcsc (θ + ∏) = - csc θsec (θ + ∏) = - sec θcot (θ + ∏) = + cot θsin (θ + 2∏) = + cos θcos (θ + 2∏) = + sin θtan (θ + 2∏) = + cot θcsc (θ + 2∏) = + sec θsec (θ + 2∏) = + csc θcot (θ + 2∏) = + tan θ