Come si risolve l equazione tanx=-tan(x-2/5pi)?

-------------------------------------------------------

answers:
Como say: What is meant :-
tan x = tan [ x - (2/5) π ] ????????
or
tan x = tan [ (x - 2) / (5π) ] ???????
-
Captain Matticus, LandPiratesInc say: tan(x) = -tan(x - (2/5)* pi)
tan(x) = tan((2/5)* pi - x)

Remember, tan(x) is periodic to pi

tan(x + pi * k) = tan((2/5) * pi - x)
x + pi * k = (2/5) * pi - x
x + x = (2/5) * pi - pi * k
2x = pi * (2/5 - k)
x = (pi/2) * (2/5 - k)

k is an integer

0 < x < 2pi for instance

0 < (pi/2) * (2/5 - k) < 2pi
0 < (2/5 - k) < 4
-2/5 < -k < 18/5
-18/5 < k < 2/5
k = -3 , -2 , -1 , 0

x = (pi/2) * (2/5 - k)
x = (pi/2) * (2/5 - (-3)) , (pi/2) * (2/5 - (-2)) , (pi/2) * (2/5 - (-1)) , (pi/2) * (2/5 - 0)
x = (pi/2) * (2/5 + 15/5) , (pi/2) * (2/5 + 10/5) , (pi/2) * (2/5 + 5/5) , (pi/2) * (2/5)
x = (pi/2) * (17/5) , (pi/2) * (12/5) , (pi/2) * (7/5) , (pi/2) * (2/5)
x = 17pi / 10 , 6pi / 5 , 7pi / 10 , pi / 5
-
david say: tanx = -tan(x - (2/5)pi) <<<< us this what you mean??? spacing is important to show meaning
Quad 1 and 4 --- x = 2pi - (x - (2/5)pi)
x = 2pi - x + (2/5)pi
2x = (12/5)pi
x = (6/5)pi ...
-
bored_and_fat say: isn't' there a spanish/italian/portuguese yahoo answers?
-
Muke say: Figure it out yourself lazy human being
-