Trigonometry Laws And Identities

law of sines:

sin(A)/a= sin(B)/b= sin(C)/c

law of cosines:

a²=b²+ c² - 2bccosa

b²=a²+ c² - 2accosb

c²= a²+ b² - 2abcosc

Identities:

sin a=opp/hyp

cos a=adj/hyp

tan a= opp/adj

cot a= adj/opp

csc a= hyp/opp

sec a= hyp/adj

Unit Circle:

sine: y-axis

cosine: x-axis

tan=sin/cos

Large: radical(3)/2

Medium: radical(2)/2

Small: 1/2

Pythagorean’s Theorem:

a²+b²=c²

Pythagorean’s Identities:

sin²a+cos²a=1

tan²a+1=sec²a

cot²a+1=csc²a

Even/Odd Identities:

sin(-a)=-sina

cos(-a)=cosa

tan(-a)=-tana

cot (-a) = -cota

csc(-a)=-csca

sec(-a)= seca

Double Angle Identities:

sin(2a)=2sinacosa

cos(2a)=cos²a-sin²a=2cos²a-1=1-2sin²a

tan(2a)=2tana/1-tan²a

Half Angle Identities:

cos(a/2)= ±radical(1+cosa/2)

sin(a/2)= ±radical(1-cosa/2)

tan(a/2)= ±radical(1-cosa/1+cosa)