Use the unit circle to determine exact trigonometric values at quadrantal angles and angles with reference angles $\pi/6$, $\pi/4$, and $\pi/3$, apply reciprocal, quotient, Pythagorean, and compound-angle identities, and verify identities while respecting signs, domains, and undefined values. Transform and graph sine, cosine, and tangent functions, interpreting amplitude, period, phase shift, vertical displacement, midline, asymptotes, key features, and standard real-valued models of periodic phenomena. Solve trigonometric equations over specified degree or radian intervals using algebraic manipulation, identities, factoring, substitution, periodicity, quadrant relationships, inverse-trigonometric values, and verification of all solutions.