FM - Unit 4

Question 1

General Solutions for Trigonometric Equations

Answer 1

cos, x = 2nπ ± PV
sin, x = nπ + (-1)^n PV
tan, x = nπ + PV

Question 2

Roots of Unity

Answer 2

Where x^n = 1

find modulus & argument where arg(x) = (O + 2mπ) / n

Question 3

Trigonometric Equations In Complex Forms

Answer 3

cos(nO) = (z^n + z^-n)/2
sin(nO) = (z^n - z^-n)/2i

Question 4

MacLaurin Series

Answer 4

e^x = all
cos(x) = 1 - x^2/2! + x^4/4!
sin(x) = x - x^3/3! + x^5/5!
ln(1+x) = x - x^2/2 + x^3/3, (-1,1]
(1+x)^n = 1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3!, [0,1)