Problem for March 21st from the 2026 AMS Daily Epsilon of Math Calendar
Problem for March 21st from the 2026 AMS Daily Epsilon of Math Calendar
@PercyButtons3 @DailyEpsilon The 21 points t = 0, π/2, π, 3π/2, 2π, ..., 10π are all solutions because sin(t) and cos(t) equal ±1 and 0 (or 0 and ±1) at these points.
To show that there are no other solutions, let t be a point where |sin(t)| < 1 and |cos(t)| < 1. We know sin²(t) + cos²(t) = 1, and multiplying both terms in the sum by numbers less than 1, we make a sum that is less than 1