The distance traveled along the unit circle from t=0 to t=π/2 equals which value?

The distance traveled along the unit circle from t=0 to t=π/2 equals which value?

• A. π/2
• B. π
• C. π/4
• D. 1

Answer: (A)

The distance traveled along a circle equals the arc length corresponding to the swept angle. For a circle, arc length s is r times θ, where θ is in radians. On the unit circle, the radius r is 1, so s = θ. Sweeping from t = 0 to t = π/2 means a central angle of π/2 radians, giving an arc length of π/2. You can also see this as a quarter of the full circumference 2π, which is (1/4)·2π = π/2. Therefore, the distance traveled is π/2.

The distance traveled along a circle equals the arc length corresponding to the swept angle. For a circle, arc length s is r times θ, where θ is in radians. On the unit circle, the radius r is 1, so s = θ. Sweeping from t = 0 to t = π/2 means a central angle of π/2 radians, giving an arc length of π/2. You can also see this as a quarter of the full circumference 2π, which is (1/4)·2π = π/2. Therefore, the distance traveled is π/2.