Limits and Continuity — Limits of trigonometric functions

About this lesson

This unit focuses on limits of trigonometric functions, specifically when the variable approaches zero. It begins by exploring the behavior of functions like f(x) = sin x / x as x approaches 0, using tables and radian measure, and deduces the fundamental limit lim (sin x)/x = 1 as x→0. It also covers the related limit for tan x, and introduces corollaries such as lim (1 - cos x)/x = 0. The unit includes worked examples and exercises that apply these limits to more complex expressions, often using algebraic manipulation, substitution, and trigonometric identities. Students are expected to find limits of expressions involving sine, cosine, tangent, and their combinations, sometimes with constants or multiple angles. The text also mentions that the theorem has more than one proof and provides a link for further reading, and it asks whether the limit can be found when the angle is in degree measure, explaining the answer. By the end, a student should be able to compute limits of trigonometric functions as the variable approaches zero, using the fundamental limits and corollaries, and apply them to solve problems.