Question

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 1

The correct option is 2. The sine value of the function is
`-(8√(73))/(73)`.

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:

`hypotenuse=√((perpendicular)^2+(base)^2)`

`hypotenuse=√((8)^2+(3)^2)`

`hypotenuse=√(64+9)`

`hypotenuse=√(73)`

In a right angled triangle

`\sin \theta=(opposite)/(hypotenuse)`

`\sin \theta=(8)/(√(73))`

`\sin \theta=(8√(73))/(73)`

Since point (3, −8) is in 4th quadrant and sine value is negative in 4th quadrant, therefore

`\sin \theta=-(8√(73))/(73)`

The sine value of the function is
`-(8√(73))/(73)`. Therefore the correct option is 2.