Can You Have Negative Radians

Degrees to radians: In geometry, both degree and radian represent the measure of an angle. One complete anticlockwise revolution tin can be represented by 2π (in radians) or 360° (in degrees). Therefore, degree and radian tin be equated as:

2π = 360°

And

π = 180°

Hence, from the to a higher place equation, we can say, 180 degrees is equal to π radian.

Ordinarily, in general geometry, we consider the measure of the angle in degrees (°). Radian is unremarkably considered while measuring the angles of trigonometric functions or periodic functions. Radians is always represented in terms of pi, where the value of pi is equal to 22/seven or three.xiv.

Learn virtually caste measure and radian measure of angles here.

A degree has its sub-parts also, stated as minutes and seconds. This conversion is a major part of Trigonometry applications.

Degrees × (π/180) = Radians

Radians × (180/π) = Degrees

360 Degrees = 2π Radians

180 Degrees = π Radians

In this article, we are going to learn the conversion from degrees to radians, radians to degrees with its conversion process and many solved examples in detail.

Table of Contents:

- Degree to Radian Conversion
- Radian to Degree Conversion
- Equation
- Formula
- Negative Caste to Radian
- Degree to Radian Estimator
- Chart
- Common Angles
- Solved Examples
- Practice Questions
- FAQs

How to Convert Degrees to Radians?

The value of 180° is equal to π radians. To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.

Degrees to Radians Formula

Where the value of π = 22/7 or 3.14

The below steps testify the conversion of angle in degree measure to radians.

Step 1: Write the numerical value of the mensurate of an bending given in degrees

Step 2: Now, multiply the numeral value written in footstep i by π/180

Step 3: Simplify the expression by cancelling the common factors of the numerical

Pace four: The consequence obtained after the simplification volition be the bending measure in radians

Let's have a look at the examples of conversions of different angle measures.

Example 1: Convert 90 degrees to radians.

Solution: Given, 90 degrees is the angle

Angle in radian = Angle in degree x (π/180)

= 90 x (π/180)

= π/2

Hence, xc degrees is equal to π/2 in radian.

Radians to Degrees Conversion

As nosotros take already discussed, how to catechumen degrees to radians for any specific bending. Now, let us see how we tin can convert radians to degrees for whatever specific angle. The formula to catechumen radians to degrees is given past:

Radians × (180/π) = Degrees

Instance 2: Catechumen π/6 into degrees.

Solution: Using the formula,

π/6 × (180/π) = 180/6 = 30 degrees

Radian to Degree Equation

As nosotros know already, one complete revolution, counterclockwise, in an XY plane, volition exist equal to 2π (in radians) or 360° (in degrees). Therefore, both caste and radian can grade an equation, such that:

2π = 360°

π = 180°

Degrees to Radians Formula

To convert degrees to radians, we tin use the aforementioned formula as given in the above department.

Degree 10 π/180 = Radian

Allow us see some examples:

Example 3: Convert fifteen degrees to radians.

Solution: Using the formula,

15 x π/180 = π/12

Case 4: Convert 330 degrees to radians.

Solution: Using the formula,

330 x π/180 = 11π/half dozen

Negative Degrees to Radian

The method to convert a negative degree into a radian is the same as we have washed for positive degrees. Multiply the given value of the angle in degrees by π/180.

Suppose -180 degrees has to be converted into radian, then,

Radian = (π/180) x (degrees)

Radian = (π/180) x (-180°)

Angle in radian = – π

Degrees to Radians Calculator

To convert the angle value from degrees to radians, the computer will assistance in quick results.

Click here to get the degrees to radians figurer with steps.

Degrees to Radians Nautical chart

Let us create the table to convert some angles in caste form to radian form.

Bending in Degrees	Angle in Radians
0°	0
30°	π/half dozen = 0.524 Rad
45°	π/four = 0.785 Rad
sixty°	π/3 = i.047 Rad
90°	π/2 = 1.571 Rad
120°	2π/three = 2.094 Rad
150°	5π/vi = ii.618 Rad
180°	π = 3.xiv Rad
210°	7π/6 = three.665 Rad
270°	3π/2 = 4.713 Rad
360°	2π = six.283 Rad

Conversion Of Some Common Angles

Go through the tabular array below to sympathise the conversion of angles compared to the amount of turns.

Turns	Radian Measure out	Degree Measure
0 plow	0 rad	0°
i/24 plow	π/12 rad	15°
1/16 turn	π/8 rad	22.5°
1/12 turn	π/six	xxx°
one/ten turn	π/5 rad	36°
⅛ turn	π/4 rad	45°
1/2π plow	1 rad	57.3°
⅙ plough	π/iii rad	60°
⅕ plough	2π/v rad	72°
¼ turn	π/2 rad	xc°
⅓ turn	2π/iii rad	120°
⅖ turn	4π/five rad	144°
½ plough	π rad	180°
¾ turn	3π/2 rad	270°
one turn	2π rad	360°

Solved Examples

Question ane: Convert 200 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in degree × π/180

Thus,

200 degrees in radians = 200 × π/180 = 10π/9 = iii.491 Rad

Question ii: Catechumen 450 degrees into radians.

Solution: By the formula, we know;

Angle in radians = Angle in caste × π/180

Thus,

450 degrees in radians = 450 × π/180 = vii.854 Rad

Question iii: Write 3.25° in degrees, minutes and seconds.
Solution:

3.25° = three° + 0.25°

= 3° + (25/100).threescore

= three° 15′

Question 4: Catechumen 18°30'42'' into the degree.

Solution:

xviii°xxx'42'' = xviii° + (thirty/threescore)° + (42/(lx x lx))°

= 18° + 0.v° + 0.01166°

= xviii.51167°

Question 5: Find the value of 1^c in caste minute and second.

Solution: From relation we have,

(π/ii)^c = 90°

\(\brainstorm{array}{l}1^{c} = \frac{90}{(\frac{\pi }{2})^{c}}\times i^{c}\cease{array} \)

1^c = 180/π ≈ 57.2957°

≈ 57° + (0.2957 x 60)'

≈ 57° 17.742′

≈ 57° 17′ + (0.742 x lx)"

≈57° 17′ 44″

Notation – i radian is approximately 57 degrees 17 minutes and 44 seconds.

Exercise Questions

Transform 700 degrees to radians.
How many radians is equal to 100 degrees?
Catechumen 550 degrees to radians.

Oftentimes Asked Questions on Degrees to Radians

How do we convert degrees to radians?

To convert the value of the bending in degree, to its equivalent radians, nosotros need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

What is the formula to convert radian into degrees?

To catechumen the value of angle from radian to degrees, we need to multiply the given value with 180/π. For example, the value of 2π:
2π x 180/π = 360 degrees

How to convert 30 degrees to radians?

Multiply 30 degrees to π/180:
30 ten (π/180) = π/six
Hence, thirty degrees is equal to π/half-dozen in radians

How pi radians is equal to 180 degrees?

One complete revolution, counterclockwise, in an XY plane, will be equal to 2π (in radians) or 360° (in degrees). Hence, we can write:
2π = 360°
Or
π = 180°
Therefore, pi is equal to 180 degrees

What is the value of 1 degree?

I degree is equal to (π/180) ^c or 0.0174533 radians.

What is the value of one radian?

One radian is approximately equal to 57.2958 degrees or 57 degrees, 17 minutes and 44 seconds.

Catechumen 3 radians to degrees.

iii radian × 180/π = 171.887Deg

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