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

Answer:

The required cosine value of the function is: $cos{\theta}=\frac{-2\sqrt{29}}{29}$

Step-by-step 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 $cos{\theta}=\frac{Adjacent}{Hypotenuse}$

Substitute the respective values in the above formula.

$cos{\theta}=\frac{-2}{\sqrt{29}}$

$cos{\theta}=\frac{-2\sqrt{29}}{29}$

Hence, the required cosine value of the function is: $cos{\theta}=\frac{-2\sqrt{29}}{29}$