AP Precalculus 3.12 and 3.13 Formulas

sin(a + b) =

sin(a + b) =

sina(cosb) + cosa(sinb)

sin(a - b) =

sina(cosb) - cosa(sinb)

cos(a + b) =

cosa(cosb) - sina(sinb)

cos(a - b) =

cosa(cosb) + sina(sinb)

tan(a + b) =

(tana + tanb)/(1 - tana(tanb))

tan(a - b) =

(tana - tanb)/(1 + tana(tanb))

sin(2a) =

2sina(cosa)

cos(2a)= (sine formula)

1 - 2sin²(a)

cos(2a)= (cosine formula)

2cos²(a) - 1

sin²a =

(-cos(2a))/2

cos²a =

(cos(2a) + 1)/2

tan²a =

(1 - cos(2a))/(1 + cos(2a)

sin(a/2) =

±√((1 - cosa)/2)

cos(a/2) =

±√((1 + cosa)/2)

tan(a/2) = (cosine only)

±√((1-cosa)/(1 + cosa))

tan(a/2) = (cosine on top)

(1 - cosa)/(sina)

tan(a/2) = (sine on top)

(sina)/(1 + cosa)

sin²x + cos²x =

1

csc²x =

1 + cot²x

tan²x =

sec²x - 1

sec²x =

tan²x + 1

arccos x =

arcsin√(1 - x²)

arcsinx =

arccos√(1 - x²)

Convert polar to rectangular

x = rcosθ

y = rsinθ

Convert rectangular to polar (when θ is in betwen 0 and 2pi)

r = √(x² + y²)

θ = arctan (y/x)

Convert rectangular complex to polar

r = √(x² + y²), θ = arctan (y/x)

x = real number, y = coefficent of imaginary for r, full number for θ

Convert polar to rectangular complex

x = rcosθ

y = rsinθ