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Find all solutions in the interval [0,2π)

Calculus
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4 tan(3 theta) - 4 = 0

Mar 20th, 2015

tan(3theta) = 1 

3 theta = kpi+pi/4 

theta = k/3 *pi +pi/12

in [0, 2pi) these are

k=0 theta = pi/12

k=1, theta = 5pi/12

k=2, theta = 3pi/4

k=3, theta= 13pi/12

k=4, theta=17pi/12

k=5, theta = 7pi/4

Mar 20th, 2015

Where does the kpi come from?


Mar 20th, 2015

that is the general solution to tan x =1,  since tanx is peridical function with period pi, so if a is the solution for tanx = 1, then k*pi +a also a solution, with k any integer 

Mar 20th, 2015

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