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 y-values in each of the 2 graphs and assure yourself they are the reciprocal of each other.The x-intercept 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.

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

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.

Graph dictionary

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

Worksheets

Chapterwise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers