How Many Degrees Are There In One Radian Class 9 Maths CBSE

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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 MathsHow many degrees are there in one radian?AnswerVerified534.3k+ viewsHint: This problem is related to unit conversion. We need to convert one radian to degrees. These are units of angle measurement. Use the relation \[{\pi ^c}\] \[ = \] \[{180^ \circ }\].Complete step by step solution:One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. That means, the magnitude in radians of such a subtended angle is equal to the ratio of the arc length to the radius of the circle;that is: \[\theta = \dfrac{r}{s}\] Where \[\theta \] is the subtended angle in radians, \[s\] is arc length, and \[r\] is radius.A degree is a measurement of a plane angle in which one full rotation is 360 degrees.From the relation :\[{\pi ^c}\] \[ = \] \[{180^ \circ }\]\[ \Rightarrow \] \[{1^c}\] \[ = \] \[{\left( {\dfrac{{180}}{\pi }} \right)^ \circ }\]Substitute the value of \[\pi \] in the above equation:\[ \Rightarrow \] \[{1^c}\] \[ = \] \[{\left( {\dfrac{{180}}{{\left( {\dfrac{{22}}{7}} \right)}}} \right)^ \circ }\]\[ \Rightarrow \] \[{1^c}\] \[ = \] \[{\left( {\dfrac{{180 \times 7}}{{22}}} \right)^ \circ }\]\[ \Rightarrow \] \[{1^c}\] \[ \approx \] \[57.2958\]The above value is often approximated as :\[{1^c}\] \[ = \] \[{57^ \circ }\].Note:Both radian and degree are the units for measuring plane angle. A degree is symbolized by the ‘\[^ \circ \]’ symbol, while radian is symbolized by ‘\[^c\]’ symbol (both written in superscript). Radian is the S.I. unit for a plane angle.Recently Updated PagesMaster Class 9 General Knowledge: Engaging Questions & Answers for SuccessClass 9 Question and Answer - Your Ultimate Solutions GuideMaster Class 9 English: Engaging Questions & Answers for SuccessMaster Class 9 Maths: Engaging Questions & Answers for SuccessMaster Class 9 Social Science: Engaging Questions & Answers for SuccessMaster Class 9 Science: Engaging Questions & Answers for SuccessMaster Class 9 General Knowledge: Engaging Questions & Answers for SuccessClass 9 Question and Answer - Your Ultimate Solutions GuideMaster Class 9 English: Engaging Questions & Answers for SuccessMaster Class 9 Maths: Engaging Questions & Answers for SuccessMaster Class 9 Social Science: Engaging Questions & Answers for SuccessMaster Class 9 Science: Engaging Questions & Answers for Success

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