Degrees and Radians Formula
: In geometry, both degrees and radians are units used to measure angles. A full anticlockwise revolution corresponds to 2π radians or 360 degrees. This relationship can be expressed as:
2π = 360°
Furthermore,
π = 180°
Therefore, based on the above equation, it can be concluded that 180 degrees are equivalent to π radians.
Degrees And Radians Formula
Degrees and radians Formula are mathematical expressions used to convert angular measurements from one unit to another. To convert a radian into a degree we use the formula Radians = Degrees × (π / 180) and for a degree to radian we use the formula Degrees = Radians × (180 / π),
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How to Convert Degrees to Radians?
The equivalence of 180° to π radians is a fundamental relationship in angle measurement. To convert an angle from degrees to radians, you can use the following formula:
Angle in radian = Angle in degree
× π/180
Where the value of π can be approximated as 22/7 or 3.14.
Here are the steps for converting an angle from degrees to radians:
Step 1:
Begin by writing down the numerical value of the angle given in degrees.
Step 2:
Multiply the numerical value from Step 1 by π/180.
Step 3:
Simplify the expression by canceling out any common factors.
Step 4:
The result obtained after simplification will represent the angle measure in radians.
Let's go through an example to illustrate this conversion:
Example 1: Convert 90 degrees to radians.
Solution: Given an angle of 90 degrees:
Angle in radians = Angle in degrees × (π/180)
= 90 × (π/180)
= π/2
Hence, 90 degrees is equivalent to π/2 radians.
Degrees And Radians Formula Conversion
To convert radians to degrees for a specific angle, you can use the following formula:
Radians × (180/π) = Degrees
Example 2: Convert π/6 into degrees.
Solution: Using the formula,
π/6 × (180/π) = (180/6) = 30 degrees
This means that π/6 radians are equivalent to 30 degrees.
The relationship between radians and degrees can be expressed by the equation:
2π = 360°
Or
π = 180°
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Degrees And Radians Formula
To convert degrees to radians, you can use the same formula as mentioned earlier:
Degree × (π/180) = Radian
Let's look at a couple of examples:
Example 1:
Convert 15 degrees to radians.
Solution:
Using the formula,
15 × (π/180) = π/12
So, 15 degrees is equivalent to π/12 radians.
Example 2:
Convert 330 degrees to radians.
Solution:
Using the formula,
330 × (π/180) = 11π/6
Therefore, 330 degrees is equal to 11π/6 radians.
You can also convert negative degrees to radians using the same formula. For instance, if you want to convert -180 degrees to radians:
Radian = (π/180) × (degrees)
Radian = (π/180) × (-180°)
Angle in radians = -π
For quick results, you can use a degrees to radians calculator.
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Degrees And Radians Formula Chart
"Degrees and Radians Formula Chart" is a visual or written reference resource that provides a comprehensive collection of formulas and conversion factors related to angles and angular measurements in both degrees and radians.
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Degrees And Radians Formula Chart
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Angle in Degrees
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Angle in Radians
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0°
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0
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30°
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π/6 = 0.524 Rad
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45°
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π/4 = 0.785 Rad
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60°
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π/3 = 1.047 Rad
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90°
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π/2 = 1.571 Rad
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120°
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2π/3 = 2.094 Rad
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150°
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5π/6 = 2.618 Rad
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180°
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π = 3.14 Rad
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210°
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7π/6 = 3.665 Rad
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270°
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3π/2 = 4.713 Rad
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360°
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2π = 6.283 Rad
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Degrees And Radians Formula Conversion of Some Common Angles
The conversion of some common angles from degrees to radians and vice versa is a fundamental aspect of trigonometry and calculus. Here's a definition and examples of how to perform these conversions for a few frequently encountered angles:
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Degrees And Radians Formula Conversion
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Turns
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Radian Measure
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Degree Measure
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0 turn
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0 rad
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0°
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1/24 turn
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π/12 rad
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15°
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1/16 turn
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π/8 rad
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22.5°
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1/12 turn
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π/6
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30°
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1/10 turn
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π/5 rad
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36°
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⅛ turn
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π/4 rad
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45°
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1/2π turn
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1 rad
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57.3°
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⅙ turn
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π/3 rad
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60°
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⅕ turn
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2π/5 rad
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72°
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¼ turn
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π/2 rad
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90°
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⅓ turn
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2π/3 rad
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120°
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⅖ turn
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4π/5 rad
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144°
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½ turn
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π rad
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180°
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¾ turn
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3π/2 rad
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270°
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1 turn
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2π rad
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360°
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Degrees to Radians Solved Examples
Question 1:
Convert 200 degrees into radians.
Solution:
To convert degrees to radians, use the formula:
Angle in radians = Angle in degrees × π/180
Therefore,
200 degrees in radians = 200 × π/180 = 10π/9 ≈ 3.491 radians
Question 2:
Convert 450 degrees into radians.
Solution:
Using the same formula:
Angle in radians = Angle in degrees × π/180
So,
450 degrees in radians = 450 × π/180 ≈ 7.854 radians
Question 3:
Write 3.25° in degrees, minutes, and seconds.
Solution:
To express 3.25° in degrees, minutes, and seconds:
3.25° can be broken down into 3° and 0.25°.
Since 0.25° is equivalent to 25/100 or 1/4 of a degree, it can be expressed as 15 minutes (15').
Therefore, 3.25° is equal to 3 degrees and 15 minutes (3° 15').
Question 4:
Convert 18°30’42’’ into degrees.
Solution:
To convert 18°30’42’’ into degrees:
First, convert the minutes to degrees by dividing by 60: 30/60 = 0.5°.
Then, convert the seconds to degrees by dividing by 3600: 42/(60*60) = 0.01166°.
Finally, add all the parts together:
18° + 0.5° + 0.01166° ≈ 18.51167°
