Answer to Question #223011 in Complex Analysis for Xavier

Question #223011


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


1
Expert's answer
2021-08-24T15:49:53-0400
tanx=5=>tanx=±5=>x=±arctan5+πn,nZ|\tan x|=5=>\tan x=\pm 5=>x=\pm\arctan 5+\pi n, n\in \Z

=>x=±arctan5+πn,nZ=>x=\pm\arctan 5+\pi n, n\in \Z

For [0,2π][0, 2\pi] we have


x1=arctan5,x2=πarctan5,x_1=\arctan 5, x_2=\pi-\arctan 5,

x3=arctan5+π,x4=2πarctan5.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. 



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