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The angle of rotation is often measured in revolutions. Determine how many radians are equivalent to 5.85 revolutions.

a. 36.6 radians
b. 37.5 radians
c. 37.2 radians
d. 37.8 radians

Answer :

Final answer:

To find how many radians are equivalent to 5.85 revolutions, multiply 5.85 by 2π to get 11.7π radians. Then, use the approximate value of π (3.14159) to calculate 11.7 * 3.14159 ≈ 36.8 radians. The closest answer is option a, 36.6 radians.

Explanation:

The question asks how many radians are equivalent to 5.85 revolutions. The formula to convert revolutions to radians is based on the fact that 1 revolution equals 2π radians. To find the equivalent in radians for 5.85 revolutions, we multiply 5.85 by 2π.

5.85 revolutions * 2π radians/revolution = 11.7π radians

Since π is approximately 3.14159, we then calculate 11.7 * 3.14159 ≈ 36.8 radians. Therefore, the closest answer from the given options is 36.6 radians, which makes option a the correct choice.

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