Answer

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**Hint:**For converting degree into radians we have the formula:

$p\deg = \dfrac{\pi }{{180}} \times p$

So for converting the given $ - 220$ degrees to radians we can use the above equation and instead of$p$ we just have to substitute the given value of degree.

**Complete step by step solution:**

Given

\[ - 220\deg .............................\left( i \right)\]

We know that for a full circle which is one revolution of a circle is equal to ${360^ \circ }$. Also we can equate this ${360^ \circ }$ to $2\pi $.

Such that: ${360^ \circ } = 2\pi .........................\left( {ii} \right)$

Now on dividing equation (ii) with 2 we can write:

$

\Rightarrow \dfrac{{{{360}^ \circ }}}{2} = \dfrac{{2\pi }}{2} \\

\Rightarrow {180^ \circ } = \pi .........................\left( {iii} \right) \\

$

Now from equation (iii) we can find the value of ${1^ \circ }$ and then the general formula.

Such that:

${1^ \circ } = \dfrac{\pi }{{{{180}^ \circ }}}.....................\left( {iv} \right)$

Now we have got the value of ${1^ \circ }$ such that we can write the general value for any angle $p$,

such that for an angle $p\deg $ we can write in radians as:

$p\deg = \dfrac{\pi }{{180}} \times p.............................\left( v \right)$

Now we have substituted the given value of the angle in (i) and then by simple simplification we can solve and find the value of $ - 220$ degrees in radians.

So substituting $ - 220$ degrees in equation (v) we get:

$ \Rightarrow - 220\deg = \dfrac{\pi }{{180}} \times - 220$

$

\Rightarrow - 220\deg = \dfrac{\pi }{{18}} \times - 22 \\

\Rightarrow - 220\deg = \dfrac{\pi }{9} \times - 11 \\

$

Now we know $\pi = 3.14$ so let’s substitute $\pi = 3.14$ in the above equation and find the value.

Such that:

$

\Rightarrow - 220\deg = \dfrac{{3.14}}{9} \times - 11 \\

\Rightarrow - 220\deg = - \dfrac{{34.54}}{9} \\

$

On simplifying the above equation we can find the value of$ - 220$ degrees in radians:

$ \Rightarrow - 220\deg = - 3.840$

**Therefore $ - 220$ degrees is$ - 3.840$ radians.**

**Note:**One of the most important thing which is highly useful for solving similar types of problems is the formula for converting degrees to radians which is:

$p\deg = \dfrac{\pi }{{180}} \times p$. Also it is always better to reduce the fraction and to express the fraction in decimal while representing the angle in radians.

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