Which of the following radian measures is equal to 2,880^(@) ? (The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2pi.) Choose 1 answer: (A) 4pi radians (B) 8pi radians (C) 12 pi radians (D) 16 pi radians

Understand Relationship: Understand the relationship between degrees and radians. We know that 360 degrees is equal to 2π radians. This means that 1 degree is equal to 2π/360 radians, which simplifies to π/180 radians.Convert Degrees to Radians: Convert 2,880 degrees to radians using the relationship from Step 1. Multiply 2,880 degrees by π/180 to find the equivalent in radians. 2,880 degrees * π/180 = (2,880/180) * π = 16 * π radians.Check Answer Choices: Check the answer choices to see which one matches our calculation. The correct answer is 16 * π radians.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following radian measures is equal to $2,880^{\circ}$ ? $\newline$ (The number of degrees of arc in a circle is $360^{\circ}$ . The number of radians of arc in a circle is $2\pi$ .) $\newline$ Choose $1$ answer: $\newline$ (A) $4\pi$ radians $\newline$ (B) $8\pi$ radians $\newline$ (C) $12\pi$ radians $\newline$ (D) $16\pi$ radians

View step-by-step help

Home

Math Problems

Algebra 2

Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

2,880^{\circ}

\newline

(The number of degrees of arc in a circle is

360^{\circ}

. The number of radians of arc in a circle is

2\pi

\newline

Choose

1

answer:

\newline

(A)

4\pi

radians

\newline

(B)

8\pi

radians

\newline

(C)

12\pi

radians

\newline

(D)

16\pi

radians

Understand Relationship: Understand the relationship between degrees and radians. We know that $360$ degrees is equal to $2\pi$ radians. This means that $1$ degree is equal to $\frac{2\pi}{360}$ radians, which simplifies to $\frac{\pi}{180}$ radians.
Convert Degrees to Radians: Convert $2,880$ degrees to radians using the relationship from Step $1$ . Multiply $2,880$ degrees by $\pi/180$ to find the equivalent in radians. $\newline$ $2,880$ degrees $* \pi/180 = (2,880/180) * \pi = 16 * \pi$ radians.
Check Answer Choices: Check the answer choices to see which one matches our calculation. The correct answer is $16 \times \pi$ radians.