R-formula and Trigonometry(Sean Group)
Sinx=Opposite/Hypotenus
Cosx=Adjacent/hypotenus
1 radian=180degree/π
1degree=π/180degree
1st quadrant all positive
2nd quadrant sine positive
3rd quadrant tangent positive
4th quadrant cosine positive
Trigo identites
Tanx= Opposite/adjacent
Cotx=1/tanx
secx=1/cosx
1+cot square = cosec square
cosecx=1/sinX
1+tan square= sec square
sin square x+ cos sqaure x=1
trigo ratio
sin30=1/2
sin45=1/square root 2
sin60=squareroot 3 /2
cos30=squareroot 3 /2
cos45=1/squareroot2
cos60=1/2
tan30=1/squareroot 3
tan45=1
tan60=square root 3
Addition formulae
sin(a+b)=sinacosb+cosasinb
sin(a-b)=sinacosb-cosasinb
cos(a+b)=cosacosb-sinasinb
tan(a+b)=tana+tanb/1-tanatanb
tan(a-b)=tana-tanb/1+tanatanb
cos(a-b)=cosacosb+sinasinb
Double angle formulae
sin2A=2sinAcosA
cos2A=cos square A- sin square A/ 2cos square A- 1/ 1-2sin square A
tan2A=2tanA/1-tansquare A
R-formula
asinx+bcosx=R sin(x+a)/ asinx-bcosx= Rsin(x-a)
acosx+bsinx=Rcos(x-a)/ acosx-bsinx=Rcos(x+a)
Where R=Square root of Asquare + b Square
Tan alpha = b/a