How do you find sin if tan=2?

1 Answer

Nov 27, 2015

Find sin x knowing tan x = 2

Ans: #+- (2sqrt5)/5#

Explanation:

Use the trig identity: #sin^2 x = 1/(1 + cot^2 x)#
#tan x = 2# --> #cot x = 1/2# --> #cot^2 x = 1/4#
#sin^2 x = 1/(1 + 1/4) = 1/(5/4) = 4/5#
#sin x = +- 2/sqrt5 = +- (2sqrt5)/5#

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How do you find sin if tan=2?

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