Without a calculator decide which is bigger, \( t \) or \( \sin t \) for \( 0 < t \leq \frac{\pi}{2} \). Illustrate your answer with a sketch.

5th Ed: #53

The shortest distance from a point to the \(x\)-axis is along a perpendicular line. For a point on the unit circle in the first quadrant, that distance is \( \sin t \). The distance from that same point along the arc of the circle must be longer and is \( t \).