This lecture covers the basics of trigonometric equations, including simple trigonometric equations like sin x = sin a, solving equations over specific intervals, transformation techniques, and factorization methods. The examples presented demonstrate the application of these concepts in solving equations involving trigonometric functions. The instructor illustrates the step-by-step process of solving equations such as sin(2x) = 3/4 and cos(3x + 2) = 2 cos(x) sin(-x), emphasizing the importance of domain definition and identifying solutions within specific intervals.