Question

find sin(θ) for the point (-3, -4) in standard position using the coordinate definition sin(θ) = y/r where r = √(x² + y²)

Explanation:

Step1: Calculate the value of \( r \)

Given \( x=-3 \) and \( y = -4 \), use the formula \( r=\sqrt{x^{2}+y^{2}} \).

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Step2: Calculate \( \sin(\theta) \)

Use the formula \( \sin(\theta)=\frac{y}{r} \). Substitute \( y=-4 \) and \( r = 5 \) into the formula.

$$ \sin(\theta)=\frac{-4}{5} $$

Answer:

\(-\frac{4}{5}\) (the first option)