Pre-calculus review

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sin(A + B)

sin(A)cos(B) + cos(A)sin(B)

cos(A + B)

cos(A)cos(B) - sin(A)sin(B)

tan(A + B)

tan(A) + tan(B) / 1 - tan(A)tan(B)

sin(A - B)

sin(A)cos(B) - cos(A)sin(B)

cos(A - B)

cos(A)cos(B) + sin(A)sin(B)

tan(A - B)

tan(A) - tan(B) / 1 + tan(A)tan(B)

sin(2x)

2sincos

cos(2x)

cos² - sin²

tan(2x)

2tan(x) / 1-tan²(x)

sin(x/2)

square root 1-cos / 2

cos(x/2)

square root 1+cos / 2

tan(x/2)

1-cos / sin or sin/cos + 1

Distance formula

Ellipse

Hyperbola

Where x is positive and y is negative for horizontal

Arithmetic sequence

Geometric sequence

Law of cosine

c² = a² + b² - 2abcos( c )

Parametric formulas

x = rcos(t)

y = rsin(t)

r = square root x² +y²

tan(t) = y/x

Vertices for hyperbola horizontal

(H+a, k) (H-a, k)

Foci for hyperbola

(H + or - c, k)

Where c² = a² + b²

Sum of finite series geometric

a1(1-r^n) / 1-r

Sum of a infinte series geometric

a1/ 1-r

Term of a geometric sequence

an = a1 - r^n-1

a1 can change depending on the -1

Cardioid

a +- asin(x)

Limacon

a +- b sin(x)

Flower

asin(nx)
Where if n is even then it is double the petals

Particial fraction

Where for ex. (2x-1)³, then it should be A/(2x-1) + B/(2x-1)² + C/(2x-1)³

Where for ex. (x²-2) should be Ax + B / (x²-2)

Possible rational roots

p/q where p is the last number in a equation and q is the first number in the equation.

6x³ + 5x² - 3x -2 = 0

p(-2) = 1 and 2

q(6) 1, 2, 3, 6