Explore the fundamental properties of trigonometric functions and their underlying principles in this comprehensive video lecture. Discover a powerful technique for simplifying angles greater than 2π using the period of trigonometric functions. Delve into topics such as sine range, common misconceptions, tangent, cosecant, secant, period, identities, and translation. Learn a special trick to enhance your understanding and problem-solving skills in trigonometry. Gain valuable insights from Professor Leonard's expert instruction, designed to strengthen your precalculus knowledge and prepare you for advanced mathematical concepts.