Degrees And Radians Formula, Definition, Explanation and Solved Examples

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),

Also Check: Absolute Value Formula

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°

Also Read: Linear Equation Formula

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.

Also Check: Rational Numbers Formulas

Degrees And Radians Formula Chart

Degrees And Radians Formula Conversion of Some Common Angles

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°