Evaluate using the Pythagorean identities.

Question

FInd sin x and cos x if tan x= 1/2 and sinx>0

Answer 1

Given that tan⁡(x)=1/2

sin(x)>0, we can use trigonometric identities to find sin(x) and cos(x).

We know that tan(x)=sin(x)​/cos(x), so we can write:

sin(x)​/cos(x)=1/2

From this, we can deduce that sin(x)=1 and cos(x)=2.