textbook-theory · English
The Sine and Cosine Functions
A calculus lecture note covering the graphs, properties, and derivatives of the sine and cosine functions, including periodicity, boundedness, amplitude, phase shifts, and evenness/oddness. The document derives that d/dx(sin x) = cos x and d/dx(cos x) = -sin x through graphical analysis of slopes and inflection points. Generalized forms A sin(kx) and A cos(kx) are examined, with formulas for amplitude |A| and period 2π/k, along with their derivatives.
trigonometrycalculusderivativesperiodic functions