JEE Advanced 2022: Most Important and Advanced Problems/Questions of Calculus in One-Shot | JEE 2022

Lecture 23: Calculus of Variations / Weak Form | Mathematical Methods for Engineers II | Mathematics | MIT OpenCourseWare

The functions sin θ and sin 2θ are both periodic trigonometric functions, but they differ significantly in frequency and behavior. Sin θ completes one full oscillation over an interval of 2π, while sin 2θ completes two full oscillations in the same interval, meaning it has double the frequency. This makes sin 2θ oscillate faster, with more peaks and troughs compared to sin θ. Additionally, while both functions have the same amplitude and range—from –1 to 1—their zero crossings and turning points