Answer to Question #223011 in Complex Analysis for Xavier

Question

How many angles are found in between 0 and 2π that satisfy the equation ItanxI = 5 ?

Answer 1

$$|\tan x|=5=>\tan x=\pm 5=>x=\pm\arctan 5+\pi n, n\in \Z$$

$$=>x=\pm\arctan 5+\pi n, n\in \Z$$

For $[0, 2\pi]$ we have

$$x_1=\arctan 5, x_2=\pi-\arctan 5,$$

$$x_3=\arctan 5+\pi, x_4=2\pi-\arctan 5.$$

Four angles are found in between 0 and 2π that satisfy the equation ItanxI = 5.