Mathematics

Mathematics

Problem

Is one radian greater than or less than 60∘60^{\circ}? Give a brief reason for your answer.
Intuitive explanation

The key is to convert between radians and degrees using the relationship π radians=180°\pi \text{ radians} = 180°. Since π≈3.14\pi \approx 3.14, one radian equals roughly 180°3.14≈57.3°\frac{180°}{3.14} \approx 57.3°. This comparison shows whether a radian is larger or smaller than your target angle—no calculator needed, just the fundamental conversion ratio.

Intuitive explanation

The key is to convert between radians and degrees using the relationship π radians=180°\pi \text{ radians} = 180°. Since π≈3.14\pi \approx 3.14, one radian equals roughly 180°3.14≈57.3°\frac{180°}{3.14} \approx 57.3°. This comparison shows whether a radian is larger or smaller than your target angle—no calculator needed, just the fundamental conversion ratio.

Browse the problem library