Question

the terminal side of an angle in standard position passes through \\(p(-3, -4)\\). what is the value of \\(\tan \theta\\)?

\\(\tan \theta = -\frac{4}{3}\\)

\\(\tan \theta = -\frac{3}{4}\\)

\\(\tan \theta = \frac{3}{4}\\)

\\(\tan \theta = \frac{4}{3}\\)

Explanation:

Identify coordinates of the point on the terminal side

$$ x = -3, \quad y = -4 $$

Apply the trigonometric ratio formula for tangent

$$ \tan\theta = \frac{y}{x} $$

Substitute the coordinates and simplify

$$ \tan\theta = \frac{-4}{-3} = \frac{4}{3} $$

Answer:

• (A) \(\tan\theta = -\frac{4}{3}\)
• (B) \(\tan\theta = -\frac{3}{4}\)
• (C) \(\tan\theta = \frac{3}{4}\)
• (D) \(\tan\theta = \frac{4}{3}\) (Correct answer)