Question

How do you evaluate $\csc \left( \pi \right)$ ?

Answer 1

Hint: For answering this question we need to evaluate the value of $\csc \left( \pi \right)=\csc \left( \pi \right)$ . From the basics of concept we know that the cosecant function is the inverse of sine function which can be mathematically given as $\csc \theta =\dfrac{1}{\sin \theta }$ . So we evaluate the value of $\csc \pi $ from the value of $\sin \pi $ .

Complete step by step solution:
Now considering from the question we have been asked to evaluate the value of $\csc \left( \pi \right)=\csc \left( \pi \right)$ .
From the basic concepts of trigonometry we know that the cosecant function is the inverse of sine function which can be mathematically given as $\csc \theta =\dfrac{1}{\sin \theta }$ .
We know that the value of sine function of pi is given as $\sin \pi =0$ .
As we know that we can obtain the value of cosecant function from the value of sine function.
We can simplify and mathematically write it as $\Rightarrow \csc \pi =\dfrac{1}{\sin \pi }$ .
So we can have the value as $\Rightarrow \csc \pi =\dfrac{1}{0}\Rightarrow \infty $ .

Therefore we can conclude that the value of cosecant function of pi value is given as $\csc \pi $ is undefined.

Note: While answering questions of this type we should be sure with our concept. This is a very simple question and we can solve it within a less span of time. In this question, there is less possibility of making mistakes. Similarly we can find the value of any trigonometric functions. For example consider $\cos \pi $ we can evaluate by using the formula $\cos \theta =\sqrt{1-{{\sin }^{2}}\theta }$ which can be given as $\cos \pi =-1$ since it lies in second quadrant.