Question

The radius of the circle below intersects the unit circle at 5.5. What is the approximate value of 8?

(–1,0) π
Y
(0, 1)
Z
2
0
r=1
37
2
(0, -1)
[Not drawn to scale]
0
(1,0)

Answer 1

Explanation:

To find the approximate value of θ, we can use the concept of trigonometric ratios in a right triangle.

In the given diagram, the radius intersects the unit circle at the point (0, 1). This means that the angle formed between the positive x-axis and the radius is θ.

We can see that the adjacent side of the right triangle formed is 1, and the hypotenuse is the radius of the circle, which is given as 5.5.

Using the cosine function, we have:

cos(θ) = adjacent / hypotenuse

cos(θ) = 1 / 5.5

To find θ, we can take the inverse cosine (arccos) of both sides:

θ = arccos(1 / 5.5)

Using a calculator to evaluate the arccos(1 / 5.5), we find:

θ ≈ 1.447 radians (rounded to three decimal places)

Therefore, the approximate value of θ is approximately 1.447 radians.