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Cosecant GraphCosecant Graph : We know that (cosec)csc x = 1 / sin x.It is a reciprocal of sine. When the sine function is zero then the cosec is undefined. When the sine function is maximum at 1, cosec is minimum at 1 and when sine function is minimum at 1, the cosec is maximum at 1. The sine function has period 2π so the cosec function has also period 2π.As cosec is a reciprocal of sine function so for some values this function is discontinuous. There are vertical asymptotes in cosec graph.The asymptote repeats after every π units. We know that csc x ≤ 1 or csc ≥ 1. First, we graph y = sin x and then y = csc x immediately below it. Compare the yvalues in each of the 2 graphs and assure yourself they are the reciprocal of each other.The xintercept of y=sin x and the asymptotes of y = csc x are same. The cosec graph is a ∪ shaped graph. There is no amplitude for this graph. Phase shift : y= csc(bx + c) b and c are responsible for phase shift. Phase shift means the graph will shift towards left or right side from its normal position.The displacement of the graph is based on bx + c. Make this equal to zero and solve for x. bx + c = 0 bx = c x = c/b So the Phase shift = c/b Example : If y = csc(x +2) then first graph y = sin (x +2). For y = sin (x +2) Phase shift is c/b where c = 2 and b = 1(coefficient of x). ∴ Phase shift = 2 so the sine graph will shift 2 units to left side. So the csc graph will also shift towards left by 2. cosecant graph Graph dictionary Home Page
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