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eprice32315
11.01.2020 •
Mathematics
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)
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Ответ:
Option A. -(
)
Step-by-step explanation:
Equation of a given line is a + 4b = 0 or b = -![\frac{1}{4}a](/tpl/images/0450/2526/0c629.png)
This in the form of y = mx + b, which is slope-intercept form.
Here slope of the line is (
).
Or tanθ =![\frac{(-1)}{4}](/tpl/images/0450/2526/cb49f.png)
This line coincides with the terminal side of the angle in standard position where cosθ > 0
Since tanθ =![\frac{\text{Height}}{\text{Base}}](/tpl/images/0450/2526/bd6ba.png)
and sinθ =![\frac{\text{height}}{\txt{Hypotenuse}}](/tpl/images/0450/2526/f83e3.png)
Hypotenuse =![\sqrt{\text{height}^{2}+\text{Base}^{2}}](/tpl/images/0450/2526/c77ca.png)
=![\sqrt{(1^{2}+4^{2})}](/tpl/images/0450/2526/ce3c5.png)
=![\sqrt{17}](/tpl/images/0450/2526/d21ea.png)
Since tanθ is negative and cosθ > 0 that means θ lie in fourth quadrant.
Therefore, sinθ will be negative.
[
]
sinθ = -![\frac{1}{\sqrt{17}}](/tpl/images/0450/2526/33d56.png)
= -![\frac{1}{\sqrt{17}}\times \frac{\sqrt{17} }{\sqrt{17}} = -\frac{\sqrt{17}}{17}](/tpl/images/0450/2526/7f1a6.png)
Answer will be option A.
Ответ: