Question

How do you convert $\dfrac{{43\pi }}{{18}}$ into degrees?

Answer 1

We use the formula of conversion of an angle from radians to degrees. Use unitary method first to calculate the value of unit radian into degrees and then again use unitary method to calculate the value of given angle into degrees by multiplying unit value of radian into degrees by number required.

• $\pi$ radians $= {180^ \circ }$
• Unitary method helps us to calculate the value of a single unit by dividing the value of multiple units by the number of units given.
• Unitary method helps us to calculate the value of multiple units by multiplying value of single unit to number of units given

Complete step-by-step solution:
We know that $\pi$ radians $= {180^ \circ }$
Then we use a unitary method to calculate the value of 1 radian by dividing both sides of the conversion by $\pi$.
Since $\pi$ radians $= {180^ \circ }$
$\Rightarrow 1$ radian $= \left( {\dfrac{{180}}{\pi }} \right)$degrees……………..… (1)
Now we have to calculate the value of the angle $\dfrac{{43\pi }}{{18}}$ in degrees
We use unitary method to calculate the value of given radian by multiplying the value of 1 radian by $\dfrac{{43\pi }}{{18}}$
$\Rightarrow 1 \times \dfrac{{43\pi }}{{18}}$ radian $= \left( {\dfrac{{180}}{\pi } \times \dfrac{{43\pi }}{{18}}} \right)$ degrees
Cancel same factors from numerator and denominator
$\Rightarrow \dfrac{{43\pi }}{{18}}$ radian $= {430^ \circ }$

$\therefore$Conversion of $\dfrac{{43\pi }}{{18}}$ into degrees is ${430^ \circ }$

Note: Many students get confused while converting the value of angle from radian to degree as they think the value of $\pi = {360^ \circ }$ as they think $\pi$ is the complete angle around a point, keep in mind value of $\pi = {180^ \circ }$. Also, many students leave the final answer in the unsolved form which is wrong, always cancel all possible factors from numerator and denominator and even convert the angle into decimal form if required at the end.