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
English Explanation -
There are different units used to measure angles. Each unit has a
specific purpose and application. Here are the main angle units along
with examples:
1. Degrees (°): The most commonly used unit in everyday life
and school-level geometry. A full circle has 360 degrees. Example: A right angle is 90°; a straight angle is 180°.
2. Radians (rad): Mainly used in higher mathematics,
calculus, and trigonometry. One full circle equals 2π radians. Example: 90° = π/2 radians; 180° = π radians.
3. Gradians (grad or gon): Mostly used in engineering and
surveying. A full circle has 400 gradians. Example: 100 grad = right angle; 200 grad = straight angle.
4. Turns: Used in rotation-based systems and engineering. One
turn is a complete rotation. Example: 1 turn = 360° = 2π radians.
5. Minutes and Seconds: These are subdivisions of degrees,
useful in astronomy and navigation. Example: 1° = 60′ (minutes); 1′ = 60″ (seconds); 30°15′ = 30
degrees and 15 minutes.
हिंदी में व्याख्या -
कोण को मापने के लिए विभिन्न इकाइयों का उपयोग किया जाता है। प्रत्येक इकाई
का अपना विशेष प्रयोग और उद्देश्य होता है। नीचे प्रमुख कोण इकाइयाँ और
उनके उदाहरण दिए गए हैं:
1. डिग्री (°): यह सबसे सामान्य इकाई है, जो दैनिक जीवन और
स्कूली गणित में प्रयोग होती है। एक पूरा वृत्त 360 डिग्री का होता
है। उदाहरण: समकोण = 90°; समरेख कोण = 180°
2. रेडियन (rad): यह उच्च गणित और त्रिकोणमिति में उपयोग की
जाती है। एक पूरा वृत्त 2π रेडियन का होता है। उदाहरण: 90° = π/2 रेडियन; 180° = π रेडियन
3. ग्रेडियन (grad या gon): इसका उपयोग इंजीनियरिंग और
सर्वेक्षण में अधिक होता है। एक पूर्ण वृत्त 400 ग्रेडियन का होता
है। उदाहरण: समकोण = 100 grad; समरेख कोण = 200 grad
4. टर्न (Turn): यह इकाई घूर्णन आधारित प्रणालियों और
इंजीनियरिंग में प्रयोग होती है। एक टर्न का अर्थ है पूरा घूर्णन। उदाहरण: 1 टर्न = 360° = 2π रेडियन
5. मिनट और सेकंड: ये डिग्री के उप-भाग होते हैं, और
खगोलशास्त्र एवं नेविगेशन में इनका उपयोग होता है। उदाहरण: 1° = 60′ (मिनट); 1′ = 60″ (सेकंड); 30°15′ = 30 डिग्री
15 मिनट
1. Convert 60° to radians
Step 1: Use the formula to convert degrees to radians:
(π180)
Step 2: Apply the values:
Radians = 60 × (π180)
Step 3: Simplify the expression:
Radians =
60π180
Step 4: Reduce the fraction:
Radians =
π3
Answer:π3
radians
2. Convert 1 radian to degrees
Step 1: Use the formula to convert radians to degrees:
(180π)
Step 2: Apply the values:
Degrees = 1 × (180π)
Step 3: Simplify the expression:
Degrees =
180π
Step 4: Approximate the value: Degrees ≈ 57.296°
Answer: 57.296°
3. Convert 100° to gradians
Step 1: Use the formula to convert degrees to gradians:
(109)
Step 2: Apply the values:
Gradians = 100 × (109)
Step 3: Simplify the expression:
Gradians =
10009
Step 4: Simplify the fraction: Gradians ≈ 111.11 grad
Answer: 111.11 gradians
4. Convert 200 gradians to degrees
Step 1: Use the formula to convert gradians to degrees:
(910)
Step 2: Apply the values:
Degrees = 200 × (910)
Step 3: Simplify the expression: Degrees = 180°
Answer: 180°
5. Convert 1 full turn to degrees
Step 1: 1 full turn is equal to 360° by definition.
Answer: 360°
6. Convert 0.5 turn to degrees
Step 1: Use the formula to convert turns to degrees:
Degrees = Turns × 360°
Step 2: Apply the values: Degrees = 0.5 × 360°
Step 3: Simplify the expression: Degrees = 180°
Answer: 180°
7. Convert 90° to turns
Step 1: Use the formula to convert degrees to turns:
Turns = Degrees / 360°
Step 2: Apply the values: Turns = 90 / 360
Step 3: Simplify the expression: Turns = 1/4
Answer: 1/4 turn
8. Convert 1 radian to turns
Step 1: Use the formula to convert radians to turns:
Turns = Radians / 2π
Step 2: Apply the values: Turns = 1 / 2π
Step 3: Simplify the expression: Turns ≈ 0.159 turn
Answer: ≈ 0.159 turn
9. Convert 1 gradian to radians
Step 1: Use the formula to convert gradians to radians:
Radians = Gradians ×
π200
Step 2: Apply the values:
Radians = 1 ×
π200
Step 3: Simplify the expression:
Radians =
π200
Answer:π200
radians
10. Convert 1 turn to radians
Step 1: 1 turn is equal to 2π radians by definition.
Answer: 2π radians
11. Convert 30° to radians
Step 1: Use the formula to convert degrees to radians:
(π180)
Step 2: Apply the values:
Radians = 30 × (π180)
Step 3: Simplify the expression:
Radians =
30π180
Step 4: Reduce the fraction:
Radians =
π6
Answer:π6
radians
12. Convert 1/4 turn to degrees
Step 1: Use the formula to convert turns to degrees:
Degrees = Turns × 360°
Step 2: Apply the values: Degrees = 1/4 × 360°
Step 3: Simplify the expression: Degrees = 90°
Answer: 90°
13. Convert 2π radians to degrees
Step 1: Use the formula to convert radians to degrees:
Degrees = Radians ×
180π
Step 2: Apply the values:
Degrees = 2π ×
180π
Step 3: Simplify the expression: Degrees = 360°
Answer: 360°
14. Convert 100 gradians to degrees
Step 1: Use the formula to convert gradians to degrees:
Degrees = Gradians ×
910
Step 2: Apply the values:
Degrees = 100 ×
910
Step 3: Simplify the expression: Degrees = 90°
Answer: 90°
15. Convert 90° to radians
Step 1: Use the formula to convert degrees to radians:
Radians = Degrees ×
π180
Step 2: Apply the values:
Radians = 90 ×
π180
Step 3: Simplify the expression:
Radians =
90π180
Step 4: Reduce the fraction:
Radians =
π2
Answer:π2
radians
16. Convert 45° to radians
Step 1: Use the formula to convert degrees to radians:
Radians = Degrees ×
π180
Step 2: Apply the values:
Radians = 45 ×
π180
Step 3: Simplify the expression:
Radians =
45π180
Step 4: Reduce the fraction:
Radians =
π4
Answer:π4
radians
17. Convert 2π/3 radians to degrees
Step 1: Use the formula to convert radians to degrees:
Degrees = Radians ×
180π
Step 2: Apply the values:
Degrees = (2π/3) ×
180π
Step 3: Simplify the expression: Degrees = 120°
Answer: 120°
18. Convert 1.5 turns to degrees
Step 1: Use the formula to convert turns to degrees:
Degrees = Turns × 360°
Step 2: Apply the values: Degrees = 1.5 × 360°
Step 3: Simplify the expression: Degrees = 540°
Answer: 540°
19. Convert 5π/4 radians to degrees
Step 1: Use the formula to convert radians to degrees:
Degrees = Radians ×
180π
Step 2: Apply the values:
Degrees = (5π/4) ×
180π
Step 3: Simplify the expression: Degrees = 225°
Answer: 225°
20. Convert 1/8 turn to degrees
Step 1: Use the formula to convert turns to degrees:
Degrees = Turns × 360°