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Graphs of the Other Circular Functions

Video Summary:

Graphs of the Cosecant and Secant Functions Cosecant values are reciprocals of the corresponding sine values. If sin x = 1, the value of csc x is 1. Similarly, if sin x = –1, then csc x = –1. When 0 < sin x < 1, then csc x > 1. Similarly, if –1 < sin x < 0, then csc x < –1. When approaches 0, the gets larger. The graph of y = csc x approaches the vertical line x = 0. In fact, the vertical asymptotes are the lines x = n. Cosecant Function Discontinuous at values of x of the form x = n, and has vertical asymptotes at these values. No x-intercepts. Its period is 2 with no amplitude. Symmetric with respect to the origin, and is an odd function. Secant Function Discontinuous at values of x of the form (2n + 1) , and has vertical asymptotes at these values. No x-intercepts. Its period is 2 with no amplitude. Symmetric with respect to the y-axis, and is an even function.