Question

A circle with radius of 63,010 μm is centered at the origin of a
CCS. Angles α and β are in standard position, α = 1.100 radians, and β =
1.257 radians.
a) What is the length of the arc that is captured between α and β?

Answer 1

Question 1.

A circle with radius of $63.010\mu m$ is centered at the origin of a CCS. Angles $\alpha$ and $\beta$ are in standard position, $\alpha=1.100$ radians, and $\beta=1.257$ radians. What is the length of the arc that is captured between $\alpha$ and $\beta$.

Solution. The arc between $\alpha$ and $\beta$ connects the endpoints of the terminal sides of $\alpha$ and $\beta$. Therefore, it subtends the angle $\beta-\alpha=1.257-1.1=0.157$ radians. Thus, the length of this arc is

$(\beta-\alpha)R=0.157\cdot 63.010\approx 9.89\mu m$

Answer: $\approx 9.89\mu m$. $\square$