Question

Refer to the figure below and mark all statements that are true. I A. If the measure of 9 is 0.5 radians, then the arc length is I B. If the measure of a is 60°, then the arc length is r. I c. If the ratio of the arc length to ris 1, then the measure of e is 1 radian D. The ratio of the arc length to r is always equal to

Answer 1

For A. We have:

`\begin{gathered} arc\text{ length=}r\theta \\ arc\text{ length=r (0.5)} \\ \text{arc length = r (}(1)/(2)) \\ \text{arc length = }(r)/(2) \end{gathered}`

A is True

For B. 60° = π/3 radians

`\text{arc length=}(\pi)/(3)r`

B is false

For C. We have

`\begin{gathered} \frac{arc\text{ length}}{r}=1 \\ (r\theta)/(r)=1 \\ \theta=1 \end{gathered}`

C is true

For D. We have

`\begin{gathered} \frac{arc\text{ length}}{r}=(r\theta)/(r)=\theta \\ It^(\prime)s\text{ not }\pi \end{gathered}`

D is false

Answer: A and C