precalc unit 6 formulas

height of a triangle

h/b=sinA OR h=bsinA

area of an oblique triangle

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law of cosines

heron’s area formula

standard formula for area of a triangle

1/2bh

component form of a vector

magnitude/length of a vector

vector addition formula

u + v = (u1 + v1, u2 + v2)

scalar multiple formula

ku = k(u1, u2) = (ku1, ku2)

dot product

u \* v = u1v1 + u2v2

complex number z

z = a + bi

absolute value of a complex number (z)

distance between complex numbers (z1 & z2)

midpoint between complex numbers

trig form of complex number z

z = r(cosθ + isinθ) OR rcisθ

product of 2 complex numbers

r1r2\[cos(θ1 + θ2) + isin (θ1 + θ2)\]

quotient of 2 complex numbers

r1/r2\[cos(θ1 - θ2) + isin(θ1 - θ2)\]

demoivre’s theorem

nth powers of a complex number

(a + bi)^n

nth roots of a complex number

complex number from a trig form

when z = a +bi, r = √a² + b², θ = arctan(b/a)