The function cos(theta) gives the x-coordinate of a point on the unit circle as the angle theta increases, creating a smooth wave that repeats every 2 pi units. It ranges from -1 to 1 and has a familiar wave-like shape. Cos(2theta), on the other hand, is a version of the cosine function that oscillates twice as fast—it completes two full cycles in the same interval where cos(theta) completes one. This is because the angle inside the cosine is doubled, compressing the wave. Cos(2theta) is often u

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