Answer:
D is true.
Step-by-step explanation:
We will use the formula for arc length (in radians) for this problem.
Arc length (s) = [tex]r\theta[/tex]
Where
- r is the radius
- [tex]\theta[/tex] is the angle in radians
A.
Arc length with [tex]\theta[/tex] measuring 1 and radius r is:
[tex]s=r\theta\\s=r(1)\\s=r[/tex]
So, not 2r, as stated. So A is false.
B.
Ratio of arc length to r is:
[tex]\frac{ArcLength}{r}=\frac{r\theta}{r}=\theta[/tex]
So, it's not [tex]\pi[/tex], B is false.
C.
Arc length, when [tex]\theta=60=\frac{\pi}{3}[/tex] and radius is r:
[tex]s=r\theta\\s=r(\frac{\pi}{3})=\frac{r\pi}{3}[/tex]
So, C is false.
D.
Setting up ratio of arc length to r as 1 and solving for [tex]\theta[/tex]:
[tex]\frac{ArcLength}{r}=1\\\frac{r\theta}{r}=1\\\theta=1[/tex]
D is right.
