calendar_today October 13, 2024 article 1051 words access_time 5 min replay Modified October 13, 2024 #math #calculus #parametric-curves #trigonometry #problem-solving Exploring Parametric Curves: Finding the Area of an Inner Loop Can you calculate the area enclosed by one of the inner loops formed by the curve $x(t) = 2 \cos(t) + \cos(5t)$ and $y(t) = 2 \sin(t) + \sin(5t)$?

calendar_today October 8, 2024 article 1295 words access_time 8 min replay Modified October 13, 2024 #math #induction #proof #problem-solving #inequality Breaking Down the Inequality Can you prove that the inequality holds $\forall n \ge 2$ if $x \in \left[\frac{3}{5}, 1 \right]$ and $n \in \mathbb{N}$?