Convert 1 Radian Into A Degree Minute And Second? - Vedantu

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsConvert 1 radian into a degree minute and second?AnswerVerified502.2k+ viewsHint: We describe the relation between the degree and radians, two ways to express the angles. We find the relation that 180 degrees is equal to $\pi $ radian. We express the degree value of 1 radian. We use the concept of the unitary system. We also use multiplication for the relation of ${{1}^{\circ }}$ being equal to 60 minutes and 1 minute $\left( {{1}^{'}} \right)$ is equal to 60 seconds $\left( {{1}^{''}} \right)$.Complete step by step answer:We need to find the relations between the degree and radians. There are two ways to express the angles. They are degrees and radians. The way to differentiate them is using the degree sign on the angle value.If the angle is $x$, then it means it’s $x$ radian and if it’s given ${{x}^{\circ }}$, then that means $x$ degree.The relation between these two units is that 180 degrees is equal to $\pi $ radian. The value of $\pi $ is the usual value where $\pi =3.14$. (approx.)Therefore, $\pi \text{ rad}={{180}^{\circ }}$. We also know that ${{1}^{\circ }}$ is equal to 60 minutes and 1 minute $\left( {{1}^{'}} \right)$ is equal to 60 seconds $\left( {{1}^{''}} \right)$. We can convert it into radian using the relation where 1 degree is equal to $\dfrac{\pi }{180}$ radian. This gives $x$ degree is equal to $\dfrac{\pi x}{180}$ radian. We get that 1 radian is equal to ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}$.${{\left( \dfrac{180}{\pi } \right)}^{\circ }}={{\left( 57\dfrac{3}{11} \right)}^{\circ }}$. We now convert \[{{\left( \dfrac{3}{11} \right)}^{\circ }}\] into minutes.\[{{\left( \dfrac{3}{11} \right)}^{\circ }}={{\left( \dfrac{3}{11}\times 60 \right)}^{'}}={{\left( 16\dfrac{4}{11} \right)}^{'}}\]We now convert \[{{\left( \dfrac{4}{11} \right)}^{'}}\] into seconds.\[{{\left( \dfrac{4}{11} \right)}^{'}}={{\left( \dfrac{4}{11}\times 60 \right)}^{''}}={{\left( 21\dfrac{9}{11} \right)}^{''}}\]Therefore, 1 radian is equal to \[{{57}^{\circ }}{{16}^{'}}{{\left( 21\dfrac{9}{11} \right)}^{''}}\].Note: Degrees and radians are ways of measuring angles. A radian is equal to the amount an angle would have to be open to capture an arc of the circle's circumference of equal length to the circle's radius.Recently Updated PagesBasicity of sulphurous acid and sulphuric acid areMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 11 Social Science: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for SuccessBasicity of sulphurous acid and sulphuric acid areMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 11 Social Science: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for Success

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