Question

The line with equation a + 4b = 0 coincides with the terminal side of an angle θ in standard position and cos θ > 0. What is the value of sinθ ?
a. -(√17/17)
b. -(17/√17)
c. -(14/√17)
d. -(17/√14)

Answer 1

Answer:

Option A. -($\frac{\sqrt{17}}{17}$)

Step-by-step explanation:

Equation of a given line is a + 4b = 0 or b = -$\frac{1}{4}a$

This in the form of y = mx + b, which is slope-intercept form.

Here slope of the line is ($-\frac{1}{4}$).

Or tanθ = $\frac{(-1)}{4}$

This line coincides with the terminal side of the angle in standard position where cosθ > 0

Since tanθ = $\frac{\text{Height}}{\text{Base}}$

and sinθ = $\frac{\text{height}}{\txt{Hypotenuse}}$

Hypotenuse = $\sqrt{\text{height}^{2}+\text{Base}^{2}}$

                     = $\sqrt{(1^{2}+4^{2})}$

                     = $\sqrt{17}$

Since tanθ is negative and cosθ > 0 that means θ lie in fourth quadrant.

Therefore, sinθ will be negative.

[ $\frac{-sin\theta}{+cos\theta}=-tan\theta$ ]

sinθ = -$\frac{1}{\sqrt{17}}$

       = -$\frac{1}{\sqrt{17}}\times \frac{\sqrt{17} }{\sqrt{17}} = -\frac{\sqrt{17}}{17}$

Answer will be option A.