Degree and Radian Measure Formula: Conversion & Examples

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Degree and Radian are two important units of measurement of an angle in Geometry. They are widely used in geometry for representing the value or the measure of the angles.

Radian is the SI unit of representing angular measures, especially in Trigonometric Functions.
An angle represented using Radians is equal to the length of the corresponding arc of a unit circle.
Degree is another commonly used unit of measurement of a plane angle in Geometry denoted by (°).

Degrees to Radians Conversion is done using the given formula:

Angle in Radian = Angle in Degree x π/180

Radians to Degrees Conversion is done by the given formula:

Angle in Degrees = Angle in Radians x (180/π)

Table of Content

What are Degrees and Radians?
Degreed and Radians Formula
Degrees to Radians Conversion
Radians to Degrees Conversion
Degrees and Radians Conversion Table
Degrees and Radians Chart
Things to Remember
Previous Years’ Questions
Sample Questions

Key Terms: Radians, Degrees, Trigonometric Functions, Degrees to Radians, Radians to Degrees, Geometry, Angle, Unit Circle, Rotation

What are Degrees and Radians?

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Degrees and Radians are two commonly used units of measurement of an angle. Degrees and Radians are often converted into each other depending upon the necessity in Geometry, Trigonometry, and related fields. Degree is the most commonly used unit for representing angles while Radian is used to represent the angles of trigonometric functions.

Degree is a unit of measurement of a plane angle denoted by (°).
Radian is the angle subtended at the center by an arc of length 1 unit in a unit circle.
It is calculated as Radian = Arc Length/Radius Length.
Radian is the SI unit of measurement of angles in Mathematics.
One complete rotation is 360° in Degrees and is 2π in Radians.
A 180^o angle, i.e. a straight angle is expressed as π radians.
A 90^o angle, i.e. a right angle is expressed as π/2 radians.

Degrees and Radians

Radians and Degrees

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Degrees and Radians Formula

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Degrees and Radians are the two important units used for representing the measurement of angles in Geometry. Both degrees and Radians are converted to each other depending on the situation of the problem. Here are some common values in Degrees and Radians:

360° = 2π Radians
180° = π Radians
90° = π/2 Radians

The value of an angle in Degrees can be calculated using the given value in Radians using the formula:

Angle in Degrees = Angle in Radians x (180/π)

If the value of an angle is given in Degrees, it can be calculated in Radians using the given formula:

Angle in Radian = Angle in Degree x π/180

Trigonometric Functions Detailed Video Explanation

Degrees to Radians Conversion

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Degrees to Radians Conversion is used to convert different angles given in Degrees to Radians. It is useful in measuring different angles in Geometry. The value of 360° is equal to 2π in Radians while the value of 180° is equal to π radians. Similarly, all the values given in degrees can be converted to Radians.

Degrees to Radians Conversion is done by multiplying the given value by π/180. Degrees to Radians Formula is given as:

Angle in Radian = Angle in Degree x π/180

Solved Example

Example: Convert 240° into Radians.

Solution: The given angle is 240 Degrees (240°).

Using the Degrees to Radians Formula, we get

Angle in Radian = Angle in Degree x (π/180)

Substitute the value of the given angle,

Angle in Radian = 240 × π / 180 = 4π/3

Therefore, 240 Degrees is equal to 4π/3 in Radians.

Radians to Degrees Conversion

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Radians to Degrees Conversion is almost similar to Degrees to Radians Conversion. In order to convert Radians to Degrees, multiply the given angle in Radians by 180/π.

Radians to Degrees Formula is given as follows:

Angle in Degrees = Angle in Radians x (180/π)

Solved Example

Example: Convert the angle π/5 into Degrees.

Solution: The given angle in Radians is π/5.

Using the Radians to Degrees Formula, we get

Angle in Degrees = Angle in Radians x (180/π)

Angle in Degrees = (π/5) × (180°/π )

Angle in Degrees = 180°/5 = 36°

Thus, π/5 rad is equal to 36°.

Degrees and Radians Conversion Table

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Degrees and Radians Conversion Table enlists the common radian values for the corresponding angle measures in degrees. The table helps in faster calculations when dealing with Degrees and Radians.

The conversion table for common angles in Degrees and Radians is as follows:

Angle in Degrees	Angle in Radians
0°	0
30°	30° × (π/180°) = π/6
45°	45° × (π/180°) = π/4
60°	60° × (π/180°) = π/3
90°	90° × (π/180°) = π/2
120°	120° × (π/180°) = 2π/3
150°	150° × (π/180°) = 5π/6
180°	180° × (π/180°) = π
210°	210° × (π/180°) = 7π/6
240°	240° × (π/180°) = 4π/3
270°	270° × (π/180°) = 3π/2
300°	300° × (π/180°) = 5π/3
330°	330° × (π/180°) = 11π/6
360°	360° × (π/180°) = 2π

Degrees and Radians Chart

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Degrees to Radians Chart is a graphical representation of the values of some standard angles in Degrees and Radians that can be useful for an easy and fast conversion.

Degrees to Radians Chart is given as follows:

Degrees and Radians Chart

Degrees and Radians Chart

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Things to Remember

Degree is a unit used for representing the measure of an angle in Geometry.
Radian is the SI unit of measurement of angles and is widely used for representing the angles of trigonometric functions.
One complete clockwise rotation is 2π in Radians and 360° in Degrees.
Angle in Degree = Angle in Radian × 180° / π
Angle in Radian = Angle in Degree × π / 180°
Radian is given by the formula Radian = Arc Length/Radius Length.
Radian is represented in form of pi (π) which is equal to 22/7 or 3.14.

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Sample Questions

Ques. What are Degrees and Radians? (3 Marks)

Ans. Degrees and Radians are two units of measurement of angles.

Degree is a unit used to represent angular measures or denote the angles.
Radian is the unit of measurement of angles commonly used in Trigonometric Functions.
One complete clockwise rotation is equal to 2π Radian whereas, in Degrees, one complete rotation is written as 360°.

Ques. State the Degree and Radian Formula. (3 Marks)

Ans. Radian Formula is derived from the relationship between the arc length and the radius of a unit circle. It is expressed as follows:

Radian = Arc Length/Radius Length

Radian Formula is also given in terms of Degrees as follows:

Angle in Radian: Angle in Degree × π / 180°

Degree Formula is expressed in terms of Radians as follows:

Angle in Degree: Angle in Radian × 180° / π

Ques. Convert 20° into Radians. (3 Marks)

Ans. The given angle is 20°.

Using the Degrees to Radian Conversion Formula,

Angle in Radian = Angle in Degree x (π/180)

Angle in Radian = 20 × π/180 = π/9 Radians

Thus, 20 Degrees is equal to π/9 Radians.

Ques. Convert 10° into Radians. (3 Marks)

Ans. The given angle is 10°.

According to the Degrees to Radian Conversion Formula,

Angle in Radian = Angle in Degree x (π/180)

Angle in Radian = 10 × π/180° = π/18.

Thus, 10 Degrees is equal to π/18 Radians.

Ques. Points A and B lie on a circle with center O. ∠AOB has a measure of π/4 rad. Convert the measurement of the angle from Radians to Degrees. (3 Marks)

Ans. It is given that, ∠AOB = π/4 rad

To convert, π/4 rad to Degrees, we need to use the Radians to Degrees Formula.

Angle in Radian = Angle in Degree x (π/180)

π/4 rad × (180°/π ) = (Angle in Degrees)

Angle in Degrees = 180°/4 = 45°

Thus, the measure of ∠AOB is equal to 45° in degrees.

Ques. Convert 12° into Radians. (3 Marks)

Ans. The angle is given as 12°.

Using the Degrees to Radian Conversion Formula,

Angle in Radian = Angle in Degree x (π/180)

Angle in Radian = 12 × π/180°

Angle in Radian = 12π/180° = 2π/3.

Thus, 12°is equal to 2π/3 in Radians.

Ques. Convert π/6 Radians into Degrees. (3 Marks)

Ans. The angle is given as π/6 in Radians.

Using the Radian to Degrees Conversion Formula, we get

Angle in Degrees = Angle in Radians x (180/π)

= π/6 x (180/π) = 180/6 = 30 Degrees

Thus, π/6 Radians is equal to 30 Degrees.

Ques. Convert 200 Degrees into Radians measure. (3 Marks)

Ans. The angle is given as 200 Degrees.

According to the Degrees to Radian Conversion Formula, we get

Angle in Radian = Angle in Degree x (π/180)

= 200 x (π/180) = 10π/9 = 3.491 Rad

Therefore, 200 Degrees is equal to 3.491 Radians.

Ques. How to convert 60 Degrees to Radians? (3 Marks)

Ans. 60 Degrees can be converted to Radians using the Degrees to Radian Conversion Formula.

Angle in Radian = Angle in Degree x (π/180)

= 60 x (π/180)

= π/3

Therefore, 60 Degrees is equal to π/3 in Radians.

Ques. What is π/2 in Degrees? (3 Marks)

Ans. The angle is given as π/2 in Radians.

Using the Radian to Degrees Conversion Formula, we get

Angle in Degrees = Angle in Radians x (180/π)

= π/2 x (180/π) = 180/2 = 90 Degrees

Therefore, π/2 is equal to 90 Degrees.

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Degree and Radian Measure Formula: Conversion & Examples

What are Degrees and Radians?

Degrees and Radians Formula

Degrees to Radians Conversion

Solved Example

Radians to Degrees Conversion

Solved Example

Degrees and Radians Conversion Table

Degrees and Radians Chart

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

2.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

Similar Mathematics Concepts

Comments

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Degree and Radian Measure Formula: Conversion & Examples

What are Degrees and Radians?

Degrees and Radians Formula

Degrees to Radians Conversion

Solved Example

Radians to Degrees Conversion

Solved Example

Degrees and Radians Conversion Table

Degrees and Radians Chart

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1. Find: If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

2.Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

4. Find: The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

2.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

4.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

5.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]