Inside a toy truck, there is a gear that rotates to (3, −8) when the steering wheel is turned to the left. What is the sine value of this function? 3 square root of 73 over 73 negative 8 square root of 73 over 73 3 −8

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.