If you are pursuing higher studies in Mathematics, or even in certain elementary-level contexts, there are various topics and concepts for which the angles can not be made use of the form of degrees.
For these particular subjects, the solutions are given in the terms of radians, which is unit affiliated with the circumference of a circle, the same way that the measure of angles and the value of is.
Besides that, it is not too difficult of a process. just some simple calculations and the problem is done and over with. And when solving for such solutions, only a handful of relations are to be made use of, which makes it significantly easier.
Step to Step guide to change Angles from Degree to Radian:
There are a variable number of units that are to be followed when accounting for the degree measure of an angle. If not accounted for as per the correct steps, the outcome will not be accurate. Here are the steps that are needed to be followed in the given order:
1. Account for the measure of Angle in degrees
The angle between two lines that are joined or intersected at a point in itself is a measure that is given in the terms of degrees. But for the sake of better or more accurate understanding, more precise units are also made use of. These units are called ‘minutes’ and ‘seconds’.
10=60′
1’=60″
60” (seconds) contribute to making up 1’ (minute). And, 60’ (minutes) of makeup 1° (degree).
These precise values of angles have no particular significance for elementary-level studies. But when taking into account higher mathematical formulations like Trigonometry, Differentiation, and Calculus, these transpositions and conversions become relatively significantly important. Therefore, it is necessary to know the in-between conversion of these values.
2. Use the Relation between Degrees and Radians
The relation between the measures in degree and radians can be given on the pretext of the circumference of a circle of unit radius. For this particular kind of circle, the perimeter or the circumference will be given as 2.
Therefore, 3600=2π
And, 10=180 radians
This is the particular formula that will be used to convert the measures of angles from degrees to radians.
3. Conversion from Degree to Radian
For the conversion of angles from degree to radian , the base form of the mathematical formula will be made use of. To convert, the angle measure that we are already provided with will be multiplied with 180.
4. The calculation for the solution
To solve for the answer to the conversion, the simple scalar multiplication and unitary division methods are to be made use of. By using only these methods, a person can reach an accurate conclusion or the solution to the problem.
The solution to these kinds of conversions can be in the form of integral multiples or the form of fractions. In all cases, the answer shall stand true to the solution.
However, the solution to these kinds of problems can never be in the negative direction; the solution will not be a negative quantity.
5. Units of the solution
Unlike the degrees of which unit is given as (read as degrees0, the radian measure does not support a particular symbol or unit to denote it. Therefore, in place of the unit, radians are used. The units of degrees in the form of radians can also be given in the form of ‘rad.’.
The necessity of the conversion of Degree to Radian
- These types of conversions are essentially important when the problems come into the form of the measure of the length of an arc in the context of mensuration. In these problems, rather than using the angles in form of degrees, its conversion into radians is needed.
- In trigonometry, the measures of angles in form of their radians help people in coming up with more relative formulas and solutions that can prove to be more helpful when concluding. And, centered around that, other operations are used.
- In integration and differentiations, the measure of is more of a centered prospect. And, in regards to this central measure, it is comparatively easier to solve problems around.
How to solve this type of Question?
There is a different set of formulas that are given to give the solution for these problems. For example, when asked for problems that are related to the length of an arc made on the circumference of a circle, or for the angle in a circle that is associated with the arc made, the following formula is used:
The length of the arc made on the perimeter of a circle = = arc angle360°*2πr
In this regard, it is necessary to keep in mind that, the arc angle that is used in the formula, needs to be in the units of radians, and not in degrees.
In trigonometry, when solving for higher-level mathematical operations, directly change the angle measure into radians by multiplying it with 180. And thereafter, the answer can be solved in the same order.
In certain problems, instead of the measure of the angle in degrees, the quantity will be in the form of minutes and seconds. If that is the case, you will need to use the relations given below to solve the answers to such questions:
10=60′
1’=60″
Some problems related to the Conversion of degrees into Radians
Convert 210° into radians.
To convert the degrees into radians, we simply needed to multiply the given angle with 180
210* 180
= 7π6
For a circle of diameter 8cm, the measure of the arc angle is given as 3, find the length of the arc that is made over the circumference of the circle.
The formula for the length of the arc is given as = arc angle360°*2πr
Therefore, the length of the arc will be = π*r3
= 4*3
Convert 240°30′ into radians.
The measure of 30’ needs to be converted into the form of degrees.
= 30’ = 12° = 0.5°
Now, solving for 240.5°:
To convert 240.5° degrees into radians = 240.5° * 180
= 1.33
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