R-formula and Trigonometry(Sean Group)

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R-formula and Trigonometry(Sean Group)

R-formula

Tan alpha = b/a

Where R=Square root of Asquare + b Square

acosx+bsinx=Rcos(x-a)/ acosx-bsinx=Rcos(x+a)

asinx+bcosx=R sin(x+a)/ asinx-bcosx= Rsin(x-a)

Double angle formulae

tan2A=2tanA/1-tansquare A

cos2A=cos square A- sin square A/ 2cos square A- 1/ 1-2sin square A

sin2A=2sinAcosA

Addition formulae

cos(a-b)=cosacosb+sinasinb

tan(a-b)=tana-tanb/1+tanatanb

tan(a+b)=tana+tanb/1-tanatanb

cos(a+b)=cosacosb-sinasinb

sin(a-b)=sinacosb-cosasinb

sin(a+b)=sinacosb+cosasinb

trigo ratio

tan60=square root 3

tan45=1

tan30=1/squareroot 3

cos60=1/2

cos45=1/squareroot2

cos30=squareroot 3 /2

sin60=squareroot 3 /2

sin45=1/square root 2

sin30=1/2

Trigo identites

sin square x+ cos sqaure x=1

1+tan square= sec square

cosecx=1/sinX

1+cot square = cosec square

secx=1/cosx

Cotx=1/tanx

Tanx= Opposite/adjacent

4th quadrant cosine positive

3rd quadrant tangent positive

2nd quadrant sine positive

1st quadrant all positive

1degree=π/180degree

1 radian=180degree/π

Cosx=Adjacent/hypotenus

Sinx=Opposite/Hypotenus