Converting between degrees and radians is a basic trigonometric skill that is required of students pursuing degrees in math, physics, engineering, and other subjects.

Degrees Definition

The most widely used unit for measuring angles is degrees. One degree is represented by each of the 360 equal segments that make up a whole circle. Degrees are especially helpful in many real-world applications, including daily geometry, surveying, and navigation, because of this split.

Radians Definition

In mathematics and the sciences, radians are used as the standard unit of angular measure. The angle formed by wrapping a circle’s radius around its circumference is equal to one radian. A complete circle has 2π radians, hence measuring angles in terms of the geometry of the circle makes sense when using radians. Many formulas and equations in mathematics are made simpler by Radians.

Formulas on Conversion Between Degrees and Radians

The below formulas to convert between degrees and radians:

Degrees to Radians

Radians = Degrees × π/180

Radians to Degrees

Degrees = Radians × 180/π

These formulas arise from the relationship that 180^o = π radians.

Example: Convert 45 degrees to radians.

Solution:

Radians = Degrees × π/180

Radians = 45° × π/180

45° in radians = (π/4)^c

Example: Convert π/4 radians to degrees.

Solution:

Radians = Degrees × 180/π

Radians = π/4 × 180/π

(π/4 radians) = 45^o

Degrees and Radians Conversion: Worksheet

Question 1: Convert 30 degrees into radians.

Solution:

Conversion from Degrees to Radians:

Radians = Degrees × π/180

Radians = 30° × π/180

30° = π/6 radians

Question 2: Convert 150 degrees into radians.

Solution:

Conversion from Degrees to Radians:

Radians = Degrees × π/180

Radians = 150° × π/180

150° = 5π/6 radians

Question 3: Convert 270 degrees into radians.

Solution:

Conversion from Degrees to Radians:

Radians = Degrees × π/180

Radians = 270° × π/180

270° = 3π/2 radians

Question 4: Convert 180 degrees into radians.

Solution:

Conversion from Degrees to Radians:

Radians = Degrees × π/180

Radians = 180° × π/180

180° = π radians

Question 5: Convert 360 degrees into radians.

Solution:

Conversion from Degrees to Radians:

Radians = Degrees × π/180

Radians = 360° × π/180

360° = 2π

Question 6: What is the angle in degrees if the radian measure is 3π/4?

Solution:

Conversion from radians to degrees:

Degrees = Radians × 180/π

Degrees = 3π/4 × 180/π

3π/4 radians = 135 degrees

Question 7: What is the angle in degrees if the radian measure is 11π/6?

Solution:

Conversion from radians to degrees:

Degrees = Radians × 180/π

Degrees = 11π/6 × 180/π

(11π/6) radians= 330 degrees

Question 8: What is the angle in degrees if the radian measure is 2π/3?

Solution:

Conversion from radians to degrees:

Degrees = Radians × 180/π

Degrees = 2π/3 × 180/π

(2π/3) radians = 120 degrees

Question 9: What is the angle in degrees if the radian measure is 5π/3?

Solution:

Conversion from radians to degrees:

Degrees = Radians × 180/π

Degrees = 5π/3 × 180/π

(5π/3) radians = 300 degrees

Question 10: What is the angle in degrees if the radian measure is 3π/2?

Solution:

Conversion from radians to degrees:

Degrees = Radians × 180/π

Degrees = 3π/2 × 180/π

(3π/2) radians = 270 degrees

Also Check,

• Degrees To Radians Calculator
• Radians to Degrees Conversion

Conversion Between Degrees and Radians Practice Questions

Q1. Convert 270 degrees to radians.

Q2. Convert 90 degrees into radians.

Q3. Find the radian measure of a 130-degree angle.

Q4. Determine the radian measure of a 200-degree angle.

Q5. Convert 1440 degrees to radians.

Q6. What is the angle in degrees if the radian measure is 7π/6?

Q7. What is the angle in degrees if the radian measure is π/3?

Q8. What is the angle in degrees if the radian measure is π/6?

FAQs on Degrees and Radians

Why is Conversion Between Degrees and Radians Important?

For the purpose of solving trigonometric issues, particularly those that include angular measurements in several units, it is necessary to convert between degrees and radians.

What is Radian?

An angular unit of measurement is a radian. It shows the angle that results from wrapping a circle’s radius around its circumference.

In What Unit of Measurement is a Full Circle?

Two radians make up a complete circle.

How do we Convert Degrees to Radians?

Multiply the degree measure by π/180.

How do we Convert Radians to Degrees?

Multiply the radian measure by 180/π.

What is the Relationship Between Degrees and Radians?

Relationship is given by the formulas:

• Radians = Degrees × π/180
• Degrees = Radians × 180/π