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

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3tan^2x-1=0

Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.

asked Sep 8, 2018 in PRECALCULUS by payton Apprentice

1 Answer

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3tan^2x-1=0

tan^2x=1/3

tanx =±1/sqrt(3)

tanx =1/sqrt(3)

tanx = tan(π/6)

x=nπ+π/6

n=0,x=π/6

n=1,x=π+π/6=7π/6

tanx =-1/sqrt(3)

tanx = tan(-π/6)

x=nπ-π/6

n=1,x=π-π/6=5π/6

n=2,x=-π/6=11π/6

n=π/6,5π/6,7π/6, and 11π/6.

answered Sep 8, 2018 by johnkelly Apprentice

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