Graphs of Secant and Cosecant Functions definitions Flashcards
Graphs of Secant and Cosecant Functions definitions
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Cosecant Reciprocal of sine; undefined where sine equals zero, resulting in vertical asymptotes on its graph. Secant Reciprocal of cosine; undefined where cosine equals zero, producing vertical asymptotes on its graph. Reciprocal Identity Relationship where one trigonometric function equals one divided by another, such as cosecant and sine. Asymptote Vertical line on a graph where a function approaches infinity due to division by zero. Period Horizontal length required for a trigonometric function to complete one full cycle. Peak Maximum point on a trigonometric graph, corresponding to the highest function value in a cycle. Valley Minimum point on a trigonometric graph, representing the lowest function value in a cycle. Transformation Modification of a graph through stretching, shifting, or compressing, affecting amplitude or period. Undefined Value Point where a function cannot be evaluated, often due to division by zero, leading to asymptotes. Integer Multiple of Pi Value expressed as nπ, where n is an integer; locations of asymptotes for cosecant graphs. Odd Multiple of Pi over Two Value expressed as (2n+1)π/2, where n is an integer; locations of asymptotes for secant graphs. Smiley Face Upward-opening curve segment on cosecant or secant graphs, occurring at peaks of the reciprocal function. Frowny Face Downward-opening curve segment on cosecant or secant graphs, occurring at valleys of the reciprocal function. Reciprocal Function Function formed by taking the reciprocal of another, such as secant from cosine or cosecant from sine. Wave Repeated oscillating pattern seen in trigonometric graphs, characterized by alternating peaks and valleys.
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