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Geometry Level 1

If x x is a real number satisfying sin ⁡ x > 0 \sin x > 0 and cos ⁡ x < 0 \cos x < 0 . What can we deduce about tan ⁡ x \tan x ?

tan ⁡ x = 0 \tan x = 0 tan ⁡ x < 0 \tan x < 0 tan ⁡ x > 0 \tan x > 0

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

tan ⁡ x = sin ⁡ x cos ⁡ x \tan x=\dfrac{\sin x}{\cos x} . A positive number divided by a negative number is negative so tan ⁡ x < 0 \tan x<0 .

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Nashita Rahman
Jun 2, 2016

sinx > 0 and cosx < 0 , therefore x lies in second quadrant . We know tan is negative in the second quadrant .

Hence, tanx < 0

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