PreCalc Final Formulas

sin (x+t)

sinxcost+cosxsint

cos (x+t)

cosxcost-sinxsint

sin (x-t)

sinxcost-cosxsint

cos (x-t)

cosxcost+sinxsint

tan (x-t)

tanx-tant/1+tanxtant

tan (x+t)

tanx+tant/1-tanxtant

sin (2θ)

2sinθcosθ

cos (2θ)

cos²θ-sin²θ

tan (2θ)

2tanθ/1-tan²θ

sin (θ/2)

±√1-cosθ/2

cos (θ/2)

±√1+cosθ/2

tanθ/2

sinθ/1+cosθ

a_n (Arithmetic)

a₁+(n-1)d

a_n (Geometric)

a₁*r^n-1

Summation of arithmetic S_n

n/2(a₁+a_n)

Summation of geometric S_n (not infinite)

a₁(1-rⁿ/1-r)

Summation of geometric S_n (infinite if |r|>1)

a₁/1-r

sin²θ

(1-cos2θ)/2

cos²θ

(1+cos2θ)/2

ZW (DeMoivre’s Theorem)

r1r2[cos(A + B)+isin(A + B)]

r(cosθ+isinθ)ⁿ (DeMoivre’s Theorem)

rⁿ[cos(nθ)+isin(nθ)]

tanθ = (convert from polar to rectangular)

y/x

cosθ = (convert from polar to rectangular)

x/r

sinθ = (convert from polar to rectangular)

y/r

r²=(convert from polar to rectangular)

x²+y²

x=(convert from polar to rectangular)

rcosθ

y=(convert from polar to rectangular)

rsinθ

Distance between polar coordinates

d²=r₁²+r₂²-2r₁r₂cos(θ₂-θ₁)

Area of a triangle

(1/2)absinc

Ellipse formula

(x-h)²/a²+(y-k)²/b²=1

Hyperbola formula

(x-h)²/a²-(y-k)²/b²=1

Parabola formula

(x-h)²=4p(y-k)

Vertices for ellipses & hyperbolas

(h±a,k) & (h,k±b)

Foci for ellipses & hyperbolas

(h±c,k) or (h,k±c)

Eccentricity

c/a or c/b

Focus for parabolas

(h,k+p) or (h+p,k)

Directrix

y=k-p or x=h-p