Question

the terminal side of an angle in standard position passes through p(15, -8). what is the value of sinθ?
○ sinθ = -15/17
○ sinθ = -8/17
○ sinθ = 8/17
○ sinθ = 15/17

Explanation:

Step1: Recall the definition of sine in standard position

For a point \( P(x, y) \) on the terminal side of an angle \( \theta \) in standard position, \( \sin\theta=\frac{y}{r} \), where \( r = \sqrt{x^{2}+y^{2}} \). Here, \( x = 15 \) and \( y=-8 \).

Step2: Calculate \( r \)

First, find \( r \) using the formula \( r=\sqrt{x^{2}+y^{2}} \). Substitute \( x = 15 \) and \( y=-8 \):

$$ r=\sqrt{15^{2}+(-8)^{2}}=\sqrt{225 + 64}=\sqrt{289}=17 $$

Step3: Calculate \( \sin\theta \)

Using the formula \( \sin\theta=\frac{y}{r} \), substitute \( y=-8 \) and \( r = 17 \):

$$ \sin\theta=\frac{-8}{17}=-\frac{8}{17} $$

Answer:

\( \sin\theta = -\frac{8}{17} \) (corresponding to the option \( \sin\theta = -\frac{8}{17} \))