To find the length of a circular arc, we can use the formula:
[tex]\[ \text{Arc Length} = r \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the central angle in radians.
Given:
- Radius, [tex]\( r = 4 \)[/tex]
- Central angle, [tex]\( \theta = \frac{3 \pi}{4} \)[/tex]
We plug these values into the formula:
[tex]\[ \text{Arc Length} = 4 \times \frac{3 \pi}{4} \][/tex]
First, simplify the multiplication inside the formula:
[tex]\[ \text{Arc Length} = 4 \times \frac{3 \pi}{4} = 3\pi \][/tex]
We know that the value of [tex]\( \pi \)[/tex] is approximately 3.141592653589793. To get the numerical result, we can multiply:
[tex]\[ \text{Arc Length} = 3 \times 3.141592653589793 \][/tex]
[tex]\[ \text{Arc Length} \approx 9.42477796076938 \][/tex]
Thus, the length of the circular arc is approximately 9.42477796076938 units.
