Radians to degrees conversion: How many degrees are contained in an angle of π/3 radians (use 180° = π radians)?

Introduction / Context:
Engineering and physics problems frequently require switching between radians and degrees. Since many wave, phase, and rotational formulas are naturally expressed in radians, fluency in conversion helps prevent downstream mistakes in AC analysis, phasors, and trigonometric calculations.

Given Data / Assumptions:

• Angle given: π/3 radians.
• Conversion identity: 180 degrees = π radians.
• Standard arithmetic; no approximations beyond the exact ratio are necessary.

Concept / Approach:
Use a proportion based on the fundamental equivalence of π radians to 180 degrees. Multiply the radian value by (180/π) to obtain degrees. This works for any radian measure and preserves exactness for rational multiples of π.

Step-by-Step Solution:

Verification / Alternative check:
You can instead note common benchmark angles: π/3 corresponds to 60° (π/6 → 30°, π/4 → 45°, π/2 → 90°). This memorized set confirms the arithmetic conversion.

Why Other Options Are Wrong:

• 6° and 27°: These result from incorrect scaling or dividing by 10 accidentally.
• 180°: That corresponds to π radians, not π/3.

Common Pitfalls:

• Using 360° = 2π but forgetting to divide both numerator and denominator appropriately.
• Dropping the π factor prematurely and mixing units.

Final Answer:
60°