Question

Convert $ - 220$ degrees to radians without a calculator.

Answer 1

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.