How to Graph the Cosecant Function?
The cosecant function is the reciprocal of the trigonometric function sine. In this guide, you will learn more about the graph of the cosecant function.

A step-by-step guide to graphing the cosecant function
The cosecant function is the reciprocal of the trigonometric function \(sin\). Since the cosecant function is the reciprocal of the \(sin\) function, we can write its formula as:
\(\color{blue}{csc (\theta)=\frac{Hypotenuse}{opposite\: side}=\frac{1}{sin\:\theta}}\)
\(cosec x\) is defined for all real numbers except for values where \(sin x\) is equal to zero. Therefore, we have vertical asymptotes at points where \(csc x\) is not defined. Also, using the values of \(sin x\), we have \(y=csc x\) as:
- When \(x = 0\), \(sin x = 0\) \(\rightarrow\) \(csc x =\) not defined
- When \(x = \frac{\pi }{6}\), \(sin x = \frac{1}{2}\)\(\rightarrow\) \(csc x = 2\)
- When \(x =\frac{\pi }{4}\), \(sin x=\frac{1}{\sqrt{2}}\)\(\rightarrow\) \(csc x = \sqrt{2}\)
- When \(x =\frac{\pi }{3}\), \(sin x= \frac{\sqrt{3}}{2}\)\(\rightarrow\) \(csc x = \frac{2}{\sqrt{3}}\)
- When \(x =\frac{\pi }{2}\), \(sin x = 1\)\(\rightarrow\) \(csc x=1\)
Therefore, by drawing the above points on a graph and connecting them together, we have the cosecant graph as follows:

Related to This Article
More math articles
- How to Write Best Fit Line Equations
- How to Find Similar Figures?
- 4th Grade FSA Math Practice Test Questions
- How to Find Average Rate of Change of a Function?
- 7th Grade Mathematics Worksheets: FREE & Printable
- 7th Grade ACT Aspire Math FREE Sample Practice Questions
- How to Prepare for the DAT Quantitative Reasoning Math Test?
- How to Solve Arithmetic Series
- Top 10 Tips to Create an ATI TEAS 7 Math Study Plan
- Full-Length 6th Grade PSSA Math Practice Test
What people say about "How to Graph the Cosecant Function? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.