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Angle Conversion - Definition, Types, Importance, Formulas

Angle Conversion


Degrees
Radians
Gradians

Angle Unit Conversion


Degrees×(π/180) = Radians
Radians(180/π) = Degrees
180 Degrees = πRadians

Definition - Angle unit conversion refers to the process of converting angles from one unit of measurement to another. Angles are typically measured in degrees, but there are several other units used to measure angles, such as radians, grads (or gradians), and turns. The most common angle unit conversions involve converting between degrees and radians, as radians are often used in advanced mathematical calculations and trigonometry.

परिभाषा - कोण इकाई रूपांतरण से तात्पर्य कोणों को माप की एक इकाई से दूसरी इकाई में परिवर्तित करने की प्रक्रिया से है। कोणों को आमतौर पर डिग्री में मापा जाता है, लेकिन कोणों को मापने के लिए कई अन्य इकाइयाँ भी उपयोग की जाती हैं, जैसे रेडियन, ग्रेड (या ग्रेडियन), और टर्न। सबसे आम कोण इकाई रूपांतरण में डिग्री और रेडियन के बीच रूपांतरण शामिल है, क्योंकि रेडियन का उपयोग अक्सर उन्नत गणितीय गणना और त्रिकोणमिति में किया जाता है




Types of Angle Units


Degree (°):

The degree is a unit of measurement for angles. A full circle is divided into 360 degrees, where each degree represents 1/360th of a complete rotation. It's the most common unit for measuring angles in everyday use.

डिग्री कोणों के माप की एक इकाई है। एक पूर्ण वृत्त को 360 डिग्री में विभाजित किया गया है, जहां प्रत्येक डिग्री पूर्ण घूर्णन का 1/360वां भाग दर्शाती है। यह रोजमर्रा के उपयोग में कोणों को मापने के लिए सबसे आम इकाई है।


Gradian (gon or grad):


  • Radian (rad):


    • 1. Degrees to Radians:

    To convert from degrees to radians, you can use the formula: 

    Radians = Degrees × (π / 180). Here, π (pi) is approximately 3.14159.

     

    2. Radians to Degrees:

    To convert from radians to degrees, you can use the formula: 

    Degrees = Radians × (180 / π).

     

    3. Degrees to Gradians:

    To convert from degrees to gradians, you can use the formula: 

    Gradians = Degrees × (10 / 9).

     

    4. Gradians to Degrees:

    To convert from gradians to degrees, you can use the formula: 

    Degrees = Gradians × (9 / 10).

     

    5. Radians to Gradians:

    To convert from radians to gradians, you need to perform a two-step conversion through degrees. Here's how you do it:

    A. Convert Radians to Degrees:

    Use the formula degrees = radians × (180 / π) to convert radians to degrees.

    B. Convert Degrees to Gradians:

    After you have the value in degrees, use the formula gradians = degrees × (10 / 9) to convert degrees to gradians.


    6. Gradians to Radians:

    To convert from gradians to radians, you also need to perform a two-step conversion through degrees:

    A. Convert Gradians to Degrees:

    Use the formula degrees = gradians × (9 / 10) to convert gradians to degrees.

    B. Convert Degrees to Radians:

    After you have the value in degrees, use the formula radians = degrees × (π / 180) to convert degrees to radians.


    Importance :
    Angle unit conversion is crucial for various fields such as physics, engineering, astronomy, and navigation. Different contexts might require different units, and conversion helps maintain consistency and accuracy in calculations and measurements.

    कोण इकाई रूपांतरण भौतिकी, इंजीनियरिंग, खगोल विज्ञान और नेविगेशन जैसे विभिन्न क्षेत्रों के लिए महत्वपूर्ण है। अलग-अलग संदर्भों के लिए अलग-अलग इकाइयों की आवश्यकता हो सकती है, और रूपांतरण गणना और माप में स्थिरता और सटीकता बनाए रखने में मदद करता है।



    • Remember to use these formulas as needed based on the conversion you want to perform.

    • Keep in mind that π (pi) is an irrational number, so you might need to use an approximation (such as 3.14159) in calculations.


    • आप जो रूपांतरण करना चाहते हैं उसके आधार पर आवश्यकतानुसार इन सूत्रों का उपयोग करना याद रखें।

    • ध्यान रखें कि π एक अपरिमेय संख्या है, इसलिए आपको गणना में एक सन्निकटन (जैसे 3.14159) का उपयोग करने की आवश्यकता हो सकती है।

      Some Basic Question


    Question 1: Convert 45 degrees to radians and gradians.

    Solution :To convert degrees to radians, 

    we use the formula: radians = degrees × (π / 180).

     Given Degrees = 45,

    Radians = 45 × (π / 180) 

    = π / 4.

    To convert degrees to gradians, 

    we use the formula: gradians = degrees × (10 / 9).

     Given Degrees = 45,

    Gradians = 45 × (10 / 9) 

    = 50.

     

    Question 2: Convert 2π radians to degrees and gradians.

    Solution :To convert radians to degrees, 

    we use the formula: degrees = radians × (180 / π).

     

    Given Radians = 2π,

    Degrees = 2π × (180 / π)

     = 360.


    To convert radians to gradians, 

    we use the formula: gradians = radians × (200 / π).

     

    Given Radians = 2π,

    Gradians = 2π × (200 / π)

     = 400.

     

    Question 3: Convert 30 degrees to radians.

    Solution :

    Given Degrees = 30,

    Radians = 30 × (π / 180) 

    = π / 6.

     

    Question 4: Convert 3.14 radians to degrees.

    Solution :

    Given Radians = 3.14,

    Degrees = 3.14 × (180 / π) 

    = 179.908°.

     

    Question 5: Convert 60 degrees to radians.

    Solution :

    Given Degrees = 60,

    Radians = 60 × (π / 180) 

    = π / 3.

     

    Question 6: Convert 0.5 radians to degrees.

    Solution :

    Given Radians = 0.5,

    Degrees = 0.5 × (180 / π) 

    = 28.647°.

     

    Question 7: Convert 90 degrees to radians.

    Solution :

    Given Degrees = 90,

    Radians = 90 × (π / 180) 

    = π / 2.

     

    Question 8: Convert 2.5 radians to degrees.

    Solution :

    Given Radians = 2.5,

    Degrees = 2.5 × (180 / π) 

    = 143.239°.

     

    Question 9: Convert 120 degrees to radians.

    Solution :

    Given Degrees = 120,

    Radians = 120 × (π / 180) 

    = 2π / 3.

     

    Question 10: Convert 1 radian to degrees.

    Solution :

    Given Radians = 1,

    Degrees = 1 × (180 / π) 

    = 57.296°.

     

    Question 11: Convert 180 degrees to radians.

    Solution :

    Given Degrees = 180,

    Radians = 180 × (π / 180) 

    = π.

     

    Question 12: Convert 4 radians to degrees.

    Solution :

    Given Radians = 4,

    Degrees = 4 × (180 / π) 

    = 229.183°.

     

    Question 13: Convert 270 degrees to radians.

    Solution :

    Given Degrees = 270,

    Radians = 270 × (π / 180) 

    = 3π / 2.

     

    Question 14: Convert 0.75 radians to degrees.

    Solution :

    Given Radians = 0.75,

    Degrees = 0.75 × (180 / π) 

    = 42.937°.

     

    Question 15: Convert 360 degrees to radians.

    Solution :

    Given Degrees = 360,

    Radians = 360 × (π / 180) 

    = 2π.

     

    Question 16: Convert 6 radians to degrees.

    Solution :

    Given Radians = 6,

    Degrees = 6 × (180 / π) 

    = 343.774°.

     

    Question 17: Convert 135 degrees to radians.

    Solution :

    Given Degrees = 135,

    Radians = 135 × (π / 180) 

    = 3π / 4.

     

    Question 18: Convert 1.5 radians to degrees.

    Solution :

    Given Radians = 1.5,

    Degrees = 1.5 × (180 / π) 

    = 85.943°.

     

    Question 19: Convert 225 degrees to radians.

    Solution :

    Given Degrees = 225,

    Radians = 225 × (π / 180) 

    = 5π / 4.

     

    Question 20: Convert 2.75 radians to degrees.

    Solution :

    Given Radians = 2.75,

    Degrees = 2.75 × (180 / π) 

    = 157.480°.



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