Question

a unit circle is shown below
$90^{\circ}=\frac{\pi}{2}$ radians. if the radius of the circle is 1, what is the approximate arc length between 0 and $\frac{\pi}{2}$ radians?
a 3.14 units
b 1.57 units
c 6.28 units
d 4.71 units

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.
Here, \( r = 1 \) and \( \theta=\frac{\pi}{2} \).

Step2: Substitute values into formula

Substitute \( r = 1 \) and \( \theta=\frac{\pi}{2} \) into \( s = r\theta \).
We get \( s = 1\times\frac{\pi}{2}=\frac{\pi}{2} \).

Step3: Approximate the value

We know that \( \pi\approx3.14 \), so \( \frac{\pi}{2}\approx\frac{3.14}{2} = 1.57 \).

Answer:

B. 1.57 units