textbook-theory · English
Differentiation of Trigonometric Functions
Section 3.5 of 'Difference Equations to Differential Equations' by Dan Sloughter, deriving the derivatives of all six trigonometric functions from first principles using limit arguments. The section establishes the fundamental limits sin(h)/h → 1 and (cos h − 1)/h → 0 via geometric squeeze-theorem reasoning, then derives the derivative rules for sin, cos, tan, cot, sec, and csc. Worked examples apply the chain rule and product rule to composite trig expressions, with a problem set and a discussion of symbolic versus numerical differentiation.
calculusdifferentiationtrigonometric functionslimits