Degrees come radians: In geometry, both degree and also radian represent the measure of an angle. One finish anticlockwise revolution can be stood for by 2π (in radians) or 360° (in degrees). Therefore, degree and also radian can be equated as:
2π = 360°
And
π = 180°
Hence, native the over equation, we have the right to say, 180 levels is equal to π radian.
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Usually, in basic geometry, we think about the measure up of the edge in levels (°). Radian is commonly considered while measuring the angle of trigonometric features or routine functions. Radians is constantly represented in terms of pi, wherein the worth of pi is same to 22/7 or 3.14.
A level has the sub-parts also, declared as minutes and also seconds. This counter is the major part that Trigonometry applications.
Degrees x π/180 = Radians Radians × 180/π = Degrees 360 degrees = 2π Radians 180 degrees = π Radians |
How to convert Degrees come Radians?
The worth of 180° is same to π radians. Come convert any type of given edge from the measure of levels to radians, the value needs to be multiplied by π/180.
Where the worth of π = 22/7 or 3.14
Below steps show the conversion of angle in degree measure to radians.
Step 1: Write the numerical value of measure up of angle given in degrees
Step 2: Now, main point the character value composed in the step 1 by π/180
Step 3: Simplify the expression through cancelling the typical factors of the numerical
Step 4: The result obtained after ~ the simplification will be the angle measure in radians
Let’s have a look in ~ the instances of switch of different angle measures.
Example 1: convert 90 levels to radians.
Solution: Given, 90 levels is the angle
Angle in radian = angle in level x (π/180)
= 90 x (π/180)
= π/2
Hence, 90 levels is same to π/2 in radian.
Radians to levels Conversion
As we have currently discussed, just how to transform degrees to radians for any certain angle. Now, let us see exactly how we can transform radians to degrees for any particular angle. The formula to transform radians to levels is provided by:
Radians × (180/π) = Degrees
Example 2: convert π/6 into degrees.
Solution: using the formula,
π/6 × (180/π) = 180/6 = 30 degrees
Radian to degree Equation
As we recognize already, one complete revolution, counterclockwise, in one XY plane, will certainly be same to 2π (in radians) or 360° (in degrees). Therefore, both degree and also radian can kind an equation, such that:
2π = 360°
Or
π = 180°
Degrees to Radian Formula
To convert degrees to radian, we can use the very same formula as given in the over section.
Degree x π/180 = Radian
Let united state see some examples:
Example 3: convert 15 degrees to radians.
Solution: using the formula,
15 x π/180 = π/12
Example 4: transform 330 degrees to radians.
Solution: utilizing the formula,
330 x π/180 = 11π/6
Negative levels to Radian
The an approach to transform a negative degree right into radian is the same as we have actually done for hopeful degrees. Multiply the provided value the the angle in degrees by π/180.
Suppose, -180 levels has to be converted into radian, then,
Radian = (π/180) x (degrees)
Radian = (π/180) x (-180°)
Angle in radian = – π
Degrees come Radians Calculator
To transform the angle value from degrees to radians, the calculator will assist in fast results.
Click below to gain the levels to radians calculator with steps.
Degrees to Radians Chart
Let us produce the table to convert some of the angle in degree kind to radian form.
Angle in DegreesAngle in Radians0° | 0 |
30° | π/6 = 0.524 Rad |
45° | π/4 = 0.785 Rad |
60° | π/3 = 1.047 Rad |
90° | π/2 = 1.571 Rad |
120° | 2π/3 = 2.094 Rad |
150° | 5π/6 = 2.618 Rad |
180° | π = 3.14 Rad |
210° | 7π/6 = 3.665 Rad |
270° | 3π/2 = 4.713 Rad |
360° | 2π = 6.283 Rad |
Solved Examples
Question 1: Convert 200 levels into radians.
Solution: by the formula, us know;
Angle in radians = edge in level × π/180
Thus,
200 levels in radians = 200 × π/180 = 10π/9 = 3.491 Rad
Question 2: convert 450 levels into radians.
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Solution: by the formula, us know;
Angle in radians = angle in degree × π/180
Thus,
450 levels in radians = 450 × π/180 = 7.854 Rad
To transform the value of angle in degree, come its tantamount radians, we have to multiply the offered value v π/180. For example, the value of 180 degrees is π in radians.
To transform the value of angle from radian come degrees, we should multiply the given value v 180/π. For example, the worth of 2π:2π x 180/π = 360 degrees