Answer :

Final answer:

The measurement of 147 can be translated into both degrees and radians. Given that 1 radian ≈ 57.3 degrees, b) 147 radians would be equivalent to 8421.1 degrees. Negative values reflect the angle's direction rather than its magnitude.

Explanation:

The measure of the angle or arc in question can be specified in both degrees and radians. One degree is known to be equivalent to approximately 0.01745 radians, and thus, 147 degrees can be converted into radians by multiplying 147 by this conversion factor (0.01745). Conversely, if the measure was originally given in radians, to find the measure in degrees, we would multiply it by approximately 57.3 degrees per radian. For the given value of 147, it can either be in degrees or radians, and if we assume it is initially in radians, then the degree measurement would be 147 multiplied by 57.3.

Therefore:

  • For 147 degrees, it remains the same in degree format.
  • For 147 radians, we would convert it to degrees by multiplying by 57.3. Hence, 147 radians x 57.3 = 8421.1 degrees.
  • For -147 degrees, it simply represents a negative angle in degrees, indicating a direction of rotation opposite to the positive angles.
  • For -147 radians, similar to the positive radian case, we convert it to degrees, which would result in -8421.1 degrees.

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