Question

There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin. What is the cosine value of this function?

Answer 1

The required cosine value of the function is:
`cos{\theta}=(-2√(29))/(29)`

Explanation:

Consider the provided information.

There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin.

Refer the figure 1:

Now from the right triangle, It is clear that the length of opposite side is 5 units and the length of adjacent side is 2 units.

Now use the Pythagoras Theorem, we get,

(2)² + (5)² = Hypotenuse²

4 + 25 = Hypotenuse²

Hypotenuse = √ 29 units.

As we know
`cos{\theta}=(Adjacent)/(Hypotenuse)`

Substitute the respective values in the above formula.

`cos{\theta}=(-2)/(√(29))`

`cos{\theta}=(-2√(29))/(29)`

Hence, the required cosine value of the function is:
`cos{\theta}=(-2√(29))/(29)`