Math 112 Identities and reference

Reciprocal Identities:

cscx= 1sinx , secx= 1

cosx , cotx= 1tanx

Quotient Identities :

tanx= sinxcosx

;cotx= cosxsinx

Pythagorean Identities:

cos2 x+sin2 x=1

1+ tan2 x=sec2 x

cot2 x+1=csc2 x

Angle Sum and Difference:

cos ( A±B )=cosAcosB∓ sinAsinB

sin ( A±B )=sinAcosB ±sinBcosA

tan ( A±B )= tanA ± tanB1∓ tanAtanB

Double Angle Identities:

sin (2θ )=2 sinθcosθ

cos (2θ )=cos2θ−sin2θ

¿2cos2θ−1

¿1−2sin2θ

tan (2θ)= 2tanθ1−tan2θ

Herons Formula:

A=√s (s−a)(s−b)(s−c)

Where s=12 (a+b+c )

Area Formula:

A=12absinC

Half Angle Identities:sin( θ2 )=±√ 1−cosθ2

cos ( θ2 )=±√ 1+cosθ2

tan( θ2 )=±√ 1−cosθ1+cosθ

Law of Sines:

sinAa

= sinBb

= sinCc

Law of Cosines:

a2=b2+c2−2bc (cosA )