Question

what is sin α?
(-√5,2)
sin α = ?

Explanation:

Step1: Recall the formula for \( r \)

For a point \((x,y)\) in the coordinate plane, \( r=\sqrt{x^{2}+y^{2}} \). Here, \( x = -\sqrt{5} \), \( y = 2 \). So \( r=\sqrt{(-\sqrt{5})^{2}+2^{2}}=\sqrt{5 + 4}=\sqrt{9}=3 \).

Step2: Recall the definition of \( \sin\alpha \)

In polar coordinates, \( \sin\alpha=\frac{y}{r} \). We know \( y = 2 \) and \( r = 3 \), so \( \sin\alpha=\frac{2}{3} \).

Answer:

\(\frac{2}{3}\)