This concept covers finding critical points (where the derivative equals zero, corresponding to horizontal tangent lines) of a linear combination of sine and cosine functions, using the derivative rules for sine and cosine together with the sum rule and constant multiple rule, and solving the resulting trigonometric equation via the tangent function and its periodicity. It also presents an alternative purely algebraic route via the angle-addition identity, which rewrites a sinx + b cosx as a single sinusoid R·sin(x + φ), reframing the critical-point question geometrically as identifying the peaks and troughs of a phase-shifted, amplitude-scaled sine graph. This belongs to single-variable calculus, at the intersection of differentiation rules for trigonometric functions and trigonometric identities, illustrating how algebraic/trigonometric restructuring can substitute for direct calculus computation.
This concept covers finding critical points (where the derivative equals zero, corresponding to horizontal tangent lines) of a linear combination of sine and cosine functions, using the derivative ru…