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1 vote
Find the x

0 \leqslant x \leqslant 360

3tan {}^(3 ) = tan \: x

1 Answer

5 votes

substitute z = tan x

rewrite


3z^3 = z\\3z^3-z = 0\\z(3z^2-1)=0


this has three solutions:

(1) z = 0

(2+3)


3z^2 = 1\\|z| = (1)/(√(3))\\


z = \pm \frac {1}{ √(3)}


So, in the range
0\leq x\leq 360 these all are solutions:

for (1) tan x is 0 for x=0, 180, and 360 degrees

for (2) tan x is 1/sqrt(3) for π/6 and 7π/6

for (3) tan x is -1/sqrt(3) for -π/6 and 5π/6

User TerryProbert
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