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?
b) To the nearest degree, what is the size of the angle between the terminal
side of α and the terminal side of β?
Section

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.

1. What is the length of the arc that is captured between $\alpha$ and $\beta$?

2. To the nearest degree, what is the size of the angle between the terminal side of $\alpha$ and the terminal side of $\beta$?

Solution. (a) 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

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

(b) We have calculated above that this angle is $\beta-\alpha=0.157$ radians. It only remains to express this angle measure in degrees:

$0.157\,radians=0.157\cdot\frac{180^{\rm o}}{\pi}\approx 9^{\rm o}.$

Answer:

1. $\approx 9.89\mu m$.

2. $\approx 9^{\rm o}$.

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