Answer:
Option A. -([tex]\frac{\sqrt{17}}{17}[/tex])
Step-by-step explanation:
Equation of a given line is a + 4b = 0 or b = -[tex]\frac{1}{4}a[/tex]
This in the form of y = mx + b, which is slope-intercept form.
Here slope of the line is ([tex]-\frac{1}{4}[/tex]).
Or tanθ = [tex]\frac{(-1)}{4}[/tex]
This line coincides with the terminal side of the angle in standard position where cosθ > 0
Since tanθ = [tex]\frac{\text{Height}}{\text{Base}}[/tex]
and sinθ = [tex]\frac{\text{height}}{\txt{Hypotenuse}}[/tex]
Hypotenuse = [tex]\sqrt{\text{height}^{2}+\text{Base}^{2}}[/tex]
= [tex]\sqrt{(1^{2}+4^{2})}[/tex]
= [tex]\sqrt{17}[/tex]
Since tanθ is negative and cosθ > 0 that means θ lie in fourth quadrant.
Therefore, sinθ will be negative.
[ [tex]\frac{-sin\theta}{+cos\theta}=-tan\theta[/tex] ]
sinθ = -[tex]\frac{1}{\sqrt{17}}[/tex]
= -[tex]\frac{1}{\sqrt{17}}\times \frac{\sqrt{17} }{\sqrt{17}} = -\frac{\sqrt{17}}{17}[/tex]
Answer will be option A.
