Question

for the problem below, \\( \theta \\) is a central angle in a circle of radius \\( r \\). find the length of arc \\( s \\) cut off by \\( \theta \\). answer exactly; do not round. \\( \theta=45^{\circ} ; \quad r=12 \\) millimeters \\( s= \\) millimeters question help: video ebook message instructor

Explanation:

Step1: Convert degree to radian

The formula to convert degrees to radians is $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$.
For $\theta = 45^{\circ}$, we have $\theta_{rad}=\frac{\pi}{180}\times45=\frac{\pi}{4}$.

Step2: Use the arc - length formula

The arc - length formula is $s = r\theta$ (where $\theta$ is in radians).
Given $r = 12$ millimeters and $\theta=\frac{\pi}{4}$, then $s=12\times\frac{\pi}{4}$.

Step3: Simplify the expression

$12\times\frac{\pi}{4}=\frac{12\pi}{4}=3\pi$.

Answer:

$3\pi$