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The number of turns performed to create the final side of the beginning side is called the angle measurement. There are various measurement units used to measure angles. The most popular units of measurement for angles are the degree measure and the radian measure. The relationship between the radian and degree measures of angles is utilised to convert the measurements of angles from one.
Degree Measure
If a turn from the beginning side to the final side equals 1/360th of a revolution, the angle is measured as one degree, which is written as 1°.
Radian Measure
The angle subtended at the centre by an arc that is 1 unit long in a circle is referred to as having the measurement of 1 radian.
Degree and Radian Measure Formula
A complete circle’s angle is 360°, which is 2p radians. This is the base for converting the measures of angles of one measurement unit into another. This means that a circle subtends an angle whose radius measure is 2p and the degree measure is 360° at the centre. It can be described as:
2p radian = 360°
or
P radius = 180°
The above equation lets us formulate a radian measure in degree measure and the degree measure in the radian measure. We are aware that the number for pi (p) would be 22/7. When we replace this number in the above equation, we get:
1 radian = 180°/p = 57° 16′ (approx)
Also,
1° = p/80 radian = 0.01746 radian (approx)
It is said that the value 180° is equivalent to the number of radians p. To convert any angle from measuring in degrees to radians, the value is multiplied by p/180.
In this case, the number of times p is 22/7, or 3.14.
The steps below show how to convert an angle from degrees to radians:
Step 1: Write down the numeric value of the measurement of an angle in degrees.
Step 2: Now, multiply the numerical value you wrote in step 1 by p/180.
Step 3: Reduce the expression by removing the common elements of the numerical.
Step 4: The product of the simplification process can be the angle measurement in Radian.
The Radian-to-Degree Equation
We already know that one complete circle clockwise in an XY plane is equal to 2p (in the radians) or 360° (in degrees).
To convert degrees to radians, we can use the same formula as described in the previous section:
Degree value * pi/180 = Radian
Properties of Degree and Radian Measure
A Degree is a measurement unit that can measure spheres, circles, and angles. A Radian can also be a measurement unit used to measure angles.
Degrees are taught in early elementary school, the beginning of high school, and then in college. Radians are taught later in the course, typically in senior high schools and colleges.
Of the two, degrees are utilised more frequently since they use basic mathematics, whereas radians employ advanced or higher maths.
A circle is 360°, which covers the total area. However, its Radian is just the half, which equals 180° or 1 pi.
Characteristics of Degree and Radian Measure
Radians and degrees are two distinct units used in the measurement of angles.
The conversion from degrees into radians is considered when taking measurements of geometric angles.
The angle measurement is usually expressed in degrees and is represented by the symbol °. An angle is determined using two distinct types of units. These are degrees and radians.
With simple formulas, you can change one type of representation of a mathematical angle to another.
The degree also has sub-parts which comprise seconds and minutes.
Conclusion
When it comes to measuring angles, degrees and radians can be used as units of measurement, but mathematicians commonly choose radians over degrees for measuring angles. Radian measurements can be utilised to calculate the area of a circle or arc length or the velocity of angular motion. It is vital to use radians when dealing with objects that move in circular directions or portions of circular paths. Even if the problem statement contains the angle expressed in degrees, we must convert those angles into the radians before applying them to any calculations.
