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Q. 72

Expert-verifiedFound in: Page 381

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

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

The approximate value of the expression $\mathrm{csc}\frac{5\pi}{13}$ is $1.07$.

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

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

- Note that $\mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta}$
- 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, $\mathrm{csc}\frac{5\pi}{13}$

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 $\mathrm{csc}$ key. Therefore we will make use of the relation, $\mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta}$

Therefore,

role="math" localid="1646330067684" $\mathrm{csc}\left(\frac{5\pi}{13}\right)=\frac{1}{\mathrm{sin}\left(\frac{5\pi}{13}\right)}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{csc}\left(\frac{5\pi}{13}\right)\approx 1.07$

which is rounded off two two decimal places.

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

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