Trig Graph Characteristics (70+ Q&A) – MATH 2026 – Domain, Range, Period, Asymptotes, Symmetry, Inverses

This A+ verified document provides over 70 questions and answers for Exam 2 of MATH 2026, focused on the graphical characteristics of the six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. It includes a full breakdown of each function's domain, range, period, symmetry (odd/even), intercepts, vertical asymptotes, and relative maxima/minima. Key identities involving inverse trig functions (e.g., sin⁻¹(sin θ) = θ and their valid domains) are also clearly addressed. The content is organized to help students understand transformation behaviors and graph features such as phase shift, reflection, and periodicity. Special attention is given to principal cycles, asymptote locations, and interval-based reasoning with integer variables, making this resource ideal for deep trig graph analysis and exam readiness. Best for: Pre-Calculus and Advanced Math students studying trig graphs and transformations College students reviewing trigonometric function properties Students preparing for graph-heavy sections of standardized tests (SAT, ACT, AP Pre-Calc) Teachers and tutors needing structured graph identity and characteristic drills Keywords: trig graphs, sine cosine tangent, cotangent secant cosecant, domain and range, trig symmetry, vertical asymptotes, inverse trig functions, trig period, relative extrema, MATH 2026, graphing trigonometric functions, even odd functions, unit circle, trig identities