Question

Help????? I don’t know which is right

Answer 1

Answer:

C

Step-by-step explanation:

Given

tanθ = $\frac{1}{2}$ = $\frac{opposite}{adjacent}$

This is a right triangle with legs 1 and 2

Using Pythagoras' identity

hypotenuse² = 1² + 2² = 1 + 4 = 5 ( take square root of both sides )

hypotenuse = $\sqrt{5}$

θ is in the 3rd quadrant where sinθ < 0 , then

sinθ = $\frac{opposite}{hypotenuse}$ = - $\frac{1}{\sqrt{5} }$ ← rationalise the denominator

       = - $\frac{1}{\sqrt{5} }$ × $\frac{\sqrt{5} }{\sqrt{5} }$

       = - $\frac{\sqrt{5} }{5}$ → C