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Trigonometric Functions and Complex Numbers covers the followings areas in the International Mathematical Olympiad (IMO) and other mathematical competitions. Trigonometric identity, graphs and properties of trigonometric equations, inverse trigonometric functions and trigonometric equations, solutions of triangles, trigonometric substitution and trigonometric inequality; The concept and operation of complex numbers, trigonometric form of a complex number, complex number and equation. The contents are essential for the IMO. A good help for students who want to improve in these areas.