Relation Between Degree and Radian

Degree

You must have heard about degrees and radians and also about the conversion of degrees to radians. So we will discuss it here. Let’s learn how to convert degrees to radians. So, One full rotation of a circle is 360° which is equal to 2π radians.

It can be written as 2π radian = 360°

π radian = 360°/2 =180°

This relationship allows us to convert a given radian measure in degree measure and a  given degree measure in radian measure. We know that the value of

pi (π) is 22/7=3.14. By putting this value,

1 radian = 180°/π = 57° 16′

We use both degree and radian to measure the angles, so there arises the question is it only degree is not enough? why do we need to use radians?

Yes, we need to use radians also, because in math we use real numbers but degrees are not expressed in numbers, They are conceptual, They are expressed using symbols like percentages. You can’t solve them without converting them to decimals.

What is a Degree?

The unit of measure for angle in mathematics is called a degree. Angle is measured by using a  protractor.  One rotation is divided into 360  parts, and each part is called a degree. It is denoted by circle °. For example, 180° means 180 degrees.

Radian Definition

The radian is equal to the amount of angle that has to be open to capture the arc of the circle’s circumference which is exactly equal to the radius of a circle is called a radian.

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Examples: What is 25% 44?

Solution:

Convert 25% to decimal

25%=0.25=25% of 44

0.25*44=11

The same is true with degrees. To solve mathematical problems, specifically in higher math, such as Calculus, should be converted to radians.

Conversion from Radian to Degree

Similar to the conversion of degrees to radians, radians to degrees can also be understood through the following examples.

Example 1: Convert the angle π/6 rad into degrees using the radians to degrees formula.

Solution: Given Radian × 180°/π = Angle in Degrees

(π/6) × (180°/π )= Angle in Degrees

Angle in degrees = 180°/6

Angle in degrees = 30°

so,π/6 rad is equal to 30° using the radians to degrees formula.

Example 2: Convert the angle 5π/12 rad into degrees using the radians to degrees formula.

Solution: Given Radian × 180°/π = Angle in Degrees

(5π/12) × (180°/π )= 5×15°

Angle in degrees = 75°

so, 5π/12 rad = 75° using the radians to degrees formula

Conversion from Degree to Radians

Example 1: Convert 60 degrees to radians.

Solution: Given, 60 degrees is the angle

radian = Given degree x (π/180)

= 60 x (π/180)

= π/3

so,60 degrees is equal to π/3 in radian.

Example 2: Convert 150 degrees to radians.

Solution: Given, 150 degrees is the angle

radian = Given degree x (π/180)

= 150 x (π/180)

= 5π/6

so, 150 degrees is equal to 5π/6  in radian

Difference Between Degree and Radian

  • It is a unit of measurement which is used to measure the circle and sphere.
  • Radian is also a unit of measurement which is to measures the angle.
  • Degrees are used in early math while radians are used in higher math concepts.
  • The degree measures how much head is tilted. Radians measure angle by distance traveled.
  • Degrees are based on the sun’s rotation. whereas radians make use of equations so radians are more reliable compared to degrees.
  • Degrees are generally used in daily life as well as in non-complex calculations as it is easy to represent and determine whereas radians are used in complex equations due to their precision.
  • Degrees are used in measuring the plane angles Radians are used in measuring the angle of 3D figures.
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