This discussion focuses on determining the continuity of trigonometric functions, specifically the six basic functions: sine, cosine, tangent, cotangent, secant, and cosecant. It is established that sine (sin(x)) and cosine (cos(x)) are continuous everywhere. In contrast, tangent (tan(x)) is discontinuous at points where its denominator, cos(x), equals zero. This pattern applies to other trigonometric functions derived from sine and cosine, indicating that discontinuities occur at specific points where their denominators are zero.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone interested in understanding the continuity properties of trigonometric functions.