Question

Arc CD is Two-thirds of the circumference of a circle. What is the radian measure of the central angle? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction radians StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians CAN YOU SHOW WORK PLEASE

Answer 1

Answer:

$\theta = \frac{4\pi}{3}$

Step-by-step explanation:

Given

Let A represent the Length of Arc CD and C, represents the circumference

$A = \frac{2}{3} C$

Required

Find the central angle (in radians)

The length of arc CD in radians is as follows;

$A = r\theta$

Where r is the radius and $\theta$ is the measure of central angle

The circumference of a circle is calculated as thus;

$C = 2\pi r$

From the question, it was stated that the arc length is 2-3rd of the circumference;

This means that

$A = \frac{2}{3} C$

Substitute $2\pi r$ for C and $r\theta$ for A

$A = \frac{2}{3} C$ becomes

$r\theta = \frac{2}{3} * 2\pi r$

$r\theta = \frac{4\pi r}{3}$

Divide both sides by r

$\frac{r\theta}{r} = \frac{4\pi r}{3}/r$

$\frac{r\theta}{r} = \frac{4\pi r}{3} * \frac{1}{r}$

$\theta = \frac{4\pi r}{3} * \frac{1}{r}$

$\theta = \frac{4\pi}{3}$

Hence, the measure of the central angle; $\theta = \frac{4\pi}{3}$

Answer 2

Answer:

The answer is C on Edge 2020

Step-by-step explanation:

I did the assignment