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Which of the following radian measures is equal to $720^\circ$ ? (The number of degrees of arc in a circle is $360^\circ$ . The number of radians of arc in a circle is $2\pi$ .)

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Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

720^\circ

? (The number of degrees of arc in a circle is

360^\circ

. The number of radians of arc in a circle is

2\pi

.)

Understand Relationship Degrees Radians: Understand the relationship between degrees and radians. We know that $360^\circ$ is equivalent to $2\pi$ radians. This means that $180^\circ$ is equivalent to $\pi$ radians. To convert degrees to radians, we use the formula $\text{radians} = \text{degrees} \times (\pi/180^\circ)$ .
Convert $720$ ° Radians: Convert $720°$ into radians using the formula from Step $1$ . By substituting $720°$ into the formula, we get $720° \times (\pi/180°) = 4\pi$ radians. This is because $720°/180° = 4$ , and $4 \times \pi = 4\pi$ .
Verify Calculation: Verify the calculation to ensure there are no math errors. We know that $360^\circ$ is $2\pi$ radians, so $720^\circ$ , which is twice $360^\circ$ , should be twice $2\pi$ radians, which is $4\pi$ radians. This confirms our calculation is correct.

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