Question

How do you convert 350 degrees to radians ? \[\]

Answer 1

Hint: We recall the definitions of degree and radian as the units to measure angles. We use the formula $R=\dfrac{\pi D}{180}$ to convert from degree to radian where D is the measure of angle in degree and R is the measure of angle in radian.\[\]

Complete step by step answer:
We know that degree is a unit for measurement of angle in a plane. If D is the measurement of the angle and it is denoted in degree with a small circle superscript $'\circ '$ as ${{D}^{\circ }}$. One degree is equal to the angle subtended at the centre by an arc of length equal to $\dfrac{1}{360}$ of circle. We also know that radian is the standard unit for measurement of angle in plane. If $R$ is the measurement of the angle in radian then it is denoted in radian with a small ‘c’ superscript symbol as ${{R}^{c}}$.1 radian is equal to the measure of angle made at the centre of a circle by an arc whose length is equal to the radius of the circle. \[\]
We convert the equal measures of angles ${{R}^{c}}$ and ${{D}^{\circ }}$into the other unit using the following formulae.
\[\begin{align}
  & {{D}^{\circ }}=\dfrac{180}{\pi }\times {{R}^{c}} \\
 & {{R}^{c}}=\dfrac{\pi }{180}\times {{D}^{\circ }} \\
\end{align}\]
 We are asked in the question to convert ${{350}^{\circ }}$ into radian. So we take $D=350$ and convert it into radian using the above formula
\[R=\dfrac{\pi }{180}\times 350=\pi \times \dfrac{350}{180}=\pi \times \dfrac{35}{18}=\pi \times 1.9\overline{4}\]
If we take approximate value $1.9\overline{4}\approx 1.94$ and $\pi =3.14$ to have
\[R\simeq 1.94\times 3.14={{6.09}^{^{c}}}\]

Note: We note that the conversion formula conversion formula comes from the equality of measure of complete angle $2{{\pi }^{c}}={{360}^{\circ }}$ where the measure ${{\pi }^{c}}$ is measure of angle subtended by a semi-circle in radian and ${{360}^{\circ }}$is the measure of circular complete angle in degree. A degree is further divided into minutes and seconds. 1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds.