Answer :
Answer:
The correct option is 2. The sine value of the function is [tex]-\frac{8\sqrt{73}}{73}[/tex].
Step-by-step explanation:
It is given that inside a toy truck, there is a gear that rotates to (3, −8) when the steering wheel is turned to the left.
Using Pythagoras theorem:
[tex]hypotenuse=\sqrt{(perpendicular)^2+(base)^2}[/tex]
[tex]hypotenuse=\sqrt{(8)^2+(3)^2}[/tex]
[tex]hypotenuse=\sqrt{64+9}[/tex]
[tex]hypotenuse=\sqrt{73}[/tex]
In a right angled triangle
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin \theta=\frac{8}{\sqrt{73}}[/tex]
[tex]\sin \theta=\frac{8\sqrt{73}}{73}[/tex]
Since point (3, −8) is in 4th quadrant and sine value is negative in 4th quadrant, therefore
[tex]\sin \theta=-\frac{8\sqrt{73}}{73}[/tex]
The sine value of the function is [tex]-\frac{8\sqrt{73}}{73}[/tex]. Therefore the correct option is 2.
