Precalculus- Identities

Cosine of a Difference

cos(A-B)=cosAcosB+sinAsinB

Sine of a Sum

sin(A+B)=sinAcosB+cosAsinB

Cosine of a Sum

cos(A+B)=cosAcosB-sinAsinB

Sine of a Difference

sin(A+B)=sinAcosB-cosAsinB

cos(x) =

sin(90-x)

sin(x)=

cos(90-x)

cot(x)=

tan(90-x)

tan(x)=

cot(90-x)

csc(x)=

sec(90-x)

sec(x)=

csc(90-x)

Tangent of a Difference

tan(A-B)= tanA-tanB / 1+ tanAtanB

Tangent of a Sum

tan(A+B)= tanA+tanB/ 1- tanAtanB

Sine Double Angle Identity

sin(2x) = 2sinxcosx

Cosine Double Angle Identity 1

cos(x+x) = cos²x-sin²x

Cosine Double Angle Identity 2

cos(2x)= 1-2sin²x

Cosine Double Angle Identity 3

cos(2x)= 2cos²-1

Tangent Double Angle

tan(2x)= 2tanx / 1-tan²x

Convert polar to rectangular coordinates

x=rcos(theta), y=rsin(theta)

Convert rectangular to polar coordinates where 0 < theta < 2pi

r = √x²+y², theta = tan^-1 (y/x)

Convert Rectangular Complex Numbers to Polar Form

r = √x²+y², tan^-1 (y/x) + pi(N)

Convert polar complex numbers to rectangular form

x= rcos(theta), y= rsin(theta)

Limaçon

r= a±bcos(theta)

Cardioid

a=b

Dimpled Cardioid

a>b

Inner loop Limaçon

a<b