Final answer:
To convert degrees into radians, multiply the number of degrees by the conversion factor (π/180), meaning the correct formula is option (a): radians = degrees * (π/180). This is verified by knowing that 1 radian is approximately equal to 57.3 degrees; multiplying 57.3 by (π/180) indeed results in 1 radian.
Step-by-step explanation:
To convert decimal degrees into radians, the correct formula is the one that takes into account the relationship between the full circle in degrees, which is 360°, and the full circle in radians, which is 2π rad. Since a full circle is equal to 360° and equivalent to 2π radians, we use this relationship to find the conversion factor. Therefore, we must multiply degrees by the conversion factor (pi/180), as the circle's 360 degrees correspond to 2π radians, so:
- a full circle (360°) corresponds to 2π rad,
- 180° corresponds to π rad,
- 1° corresponds to π/180 rad.
Given this, the correct formula to convert degrees into radians is:
radians = degrees * (π/180)
From the options given, option (a) is the correct one. To verify the correctness, you can check if the result seems reasonable. For instance, 1 radian is approximately equal to 57.3 degrees, and applying the conversion factor to 57.3 should give us a result close to 1 radian:
57.3 * (π/180) ≈ 1 radian, which confirms the correctness of option (a).
Therefore, when you choose only one option, remember to choose option (a) as your final answer.