If an angle measures π/3 radians, what is its measure in degrees?

If an angle measures π/3 radians, what is its measure in degrees?

• A. 30 degrees
• B. 60 degrees
• C. 45 degrees
• D. 120 degrees

Answer: (D)

Converting between radians and degrees uses the fact that 180 degrees equal π radians. So degrees = radians × (180/π). For π/3 radians, this is π/3 × 180/π, which simplifies to 180/3 = 60 degrees. Intuitively, since π radians is 180°, one third of π is one third of 180°, giving 60°. The other common conversions are π/6 = 30°, π/4 = 45°, and 2π/3 = 120°, which show how different fractions of π map to degrees.

Converting between radians and degrees uses the fact that 180 degrees equal π radians. So degrees = radians × (180/π). For π/3 radians, this is π/3 × 180/π, which simplifies to 180/3 = 60 degrees. Intuitively, since π radians is 180°, one third of π is one third of 180°, giving 60°. The other common conversions are π/6 = 30°, π/4 = 45°, and 2π/3 = 120°, which show how different fractions of π map to degrees.