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
- 4 Reasons To Fall In Love With Math
- 5th Grade PARCC Math FREE Sample Practice Questions
- Top 10 Pre-Algebra Prep Books (Our 2024 Favorite Picks)
- Relationship Between Sides and Angles in a Triangle
- 10 Most Common 7th Grade FSA Math Questions
- Taylor Series Uncovered: Transforming Functions into Useful Approximations
- Are knowledge checks mandatory on ALEKS?
- What are the types of math?
- How to Apply Limit Properties
- Is ALEKS just for Mathematics?
What people say about "How to Graph the Cosecant Function? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.