Question

What is the exact value of cosecant of the quantity 11 times pi over 3 end quantity question mark

Answer 1

To evaluate

`co\sec ((11\pi)/(3))`

But we need to understand the identity of cosecant

`\text{cosecant}\theta=\frac{1}{\text{sin}\theta}`
`co\sec ((11\pi)/(3))=(1)/(\sin((11\pi)/(3)))`

Simplifying further

`(1)/(\sin((11\pi)/(3)))=(1)/(\sin (660))=\frac{1}{\frac{-\sqrt[]{3}}{2}}`

`\Rightarrow\frac{-2}{\sqrt[]{3}}`

Rationalizing the denominator

`\frac{-2}{\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{-2\sqrt[]{3}}{3}`

Thus, the answer is:

`\frac{-2\sqrt[]{3}}{3}`