Question

[22π\15]© is equal to
A)246° b)264° c)224° d)426°

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\left(\dfrac{22\,\pi}{5}\right)^c}$

$\underline{\textbf{To convert:}}$

$\mathsf{\left(\dfrac{22\,\pi}{5}\right)^c\;into\;degrees}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Relation between degrees and radians}}$

$\mathsf{\pi\;radians=180^\circ}$

$\implies\boxed{\mathsf{1\;radian=\dfrac{180^\circ}{\pi}}}$

$\mathsf{Consider,}$

$\mathsf{\left(\dfrac{22\,\pi}{5}\right)^c}$

$\mathsf{=\dfrac{22\,\pi}{5}{\times}1\;radian}$

$\mathsf{=\dfrac{22\,\pi}{5}{\times}\dfrac{180^\circ}{\pi}}$

$\mathsf{=\dfrac{22}{5}{\times}180^\circ}$

$\mathsf{=22{\times}12^\circ}$

$\mathsf{=264^\circ}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(b)\;is\;correct}$

Answer 2

The correct option is (b)   $264$ °

Given:

The given equation is $\frac{22\pi }{15}$

To find:

The value of $\frac{22\pi }{15}$

Solution:

We know that the value of $\pi = 180$ °

Substituting $\pi$ value in the given equation we get,

$\frac{22\pi }{15} = (\frac{22}{15}) 180$ °

        $= 12$ × $22$

         $= 264$ °

Hence $\frac{22\pi }{15}$ is equal to  $264$ °

The correct option is (b)   $264$ °

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