Use a calculator to find the approximate value of each expression rounded to two decimal places:$\csc \frac{5\pi }{13}$

We are given an expression $\csc \frac{5\pi }{13}$

We need to find the approximate value of the expression that is rounded to two decimal places.

• Note that $\csc \theta =\frac{1}{\sin \theta }$
• While finding the values of the trigonometric functions using a calculator, we need to set the correct MODE in the calculator depending on whether the angle is in radian or in degree.

The given trigonometric expression is, $\csc \frac{5\pi }{13}$

Since the angle is in radian, we have to set the correct MODE in the calculator to receive radian.

Most of the calculators do not have $\csc$key. Therefore we will make use of the relation, $\csc \theta =\frac{1}{\sin \theta }$

Therefore,

role="math" localid="1646330067684" $$\begin{gathered} \csc \left(\frac{5\pi }{13}\right)=\frac{1}{\sin \left(\frac{5\pi }{13}\right)} \\ \Rightarrow \csc \left(\frac{5\pi }{13}\right)\approx 1.07 \end{gathered}$$

which is rounded off two two decimal places.

The approximate value of the expression$\csc \left(\frac{5\pi }{13}\right)=1.07$