If sin(x) = 2/3, what is tan(2x)?

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If sin(x) = 2/3, what is tan(2x)?

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Answer 1 · 2016-05-24T15:14:08

#4sqrt5#

Explanation:

#sin x = 2/3# , find cos x.
#cos^2 x = 1 - sin^2 x = 1 - 4/9 = 5/9#
#cos x = +- sqrt5/3#
Since x is in Quadrant I, then, cos x is positive
#cos x = sqrt5/3#
#tan x = sin x/(cos x) = (2/3)(3/sqrt5) = 2/sqrt5 = (2sqrt5)/5#
Apply the trig identity:
#tan 2x = (2tan x)/(1 - tan^2 x) #
#tan 2x = ((4sqrt5)/5)/(1 - 4/5) = (4sqrt5/5)(5/1) = 4sqrt5#

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If sin(x) = 2/3, what is tan(2x)?

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