The sine function is one of the most important ideas in trigonometry. It comes from studying right triangles, where sine is the ratio of the side opposite an angle to the hypotenuse. More broadly, sine describes patterns of oscillation, rotation, and wave motion. Its graph is a smooth, repeating curve that goes up and down between –1 and 1, repeating every 360 degrees. Because of this, sine shows up in physics to model things like sound waves, vibrations, and circular motion. The cosine function

TRIGONOMETRY IDENTITIES: Trigonometric identities are mathematical equations that are true for all values of the variables involved, where both sides of the equation are defined. They are essential tools for simplifying trigonometric expressions and solving equations. These identities are derived from the definitions of trigonometric functions and the Pythagorean theorem. MAJOR TRIGONOMETRY IDENTITIES Reciprocal Identities: These relate each trigonometric function to its reciprocal: csc θ = 1/si