Question

if tan x=1/2 and x is the third quadrant find sin x and cos x
plz reply​

Answer 1

Answer:

sin X = $\frac{1}{\sqrt[ ]{5} }$

cos X = $\frac{2}{\sqrt[ ]{5} }$

Step-by-step explanation:

∵ tan x = $\frac{1}{2}$

∵ tan x = $\frac{opposite}{adjacent}$

∴ opposite = 1  ,  adjacent = 2

∵ hypotenuse² = opposite ² + adjacent²

∴ hypotenuse = $\sqrt{1^{2}+2^{2} }$ = $\sqrt{5}$

∴ opposite = 1  ,  adjacent = 2 , hypotenuse = $\sqrt{5}$

∵ sin X = $\frac{opposite}{hypotenuse}$

∴ sin X = $\frac{1}{\sqrt[ ]{5} }$

∵ cos X = $\frac{adjacent}{hypotenuse}$

∴ cos X = $\frac{2}{\sqrt[ ]{5} }$