A radian is a standard unit of angular measurement and it is used in many areas of mathematics. The radian is represented by the symbol “rad”. In mathematical writing, the unit rad is usually omitted. If there is no symbol, radians are assumed. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2pir /r, or 2pi. Thus 2pi radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees.
There is a way to convert radians to degrees too.. All you do is multiply by 180/pi. Here’s an example.. EXAMPLE 1: pi/6 x 180/pi A). The pi(s) cancel and you get 180/6 which is 30. B). Therefore, your answer will be 30 degrees.
EXAMPLE 2: 5pi/3 x 180/pi A). The pi(s) cancel and you are left with 5/3 x 180/1. B). Therefore, your answer will be 300 degrees.
Just like you can convert radians to degrees, you can also convert degrees to radians. The formula is degrees x pi/180.
In calculus or other branches of math, angles are universally measured in radians. Why? Because radians have a mathematical “naturalness” that leads to a more elegant formation of a number of important results. Although the radian is a unit of measure, it is a dimensionless quantity. So as you can see, radians are much easier to work with. If you’re working with degrees, you’ll first have to graph it then convert it to radians.
A radian is a unit of measure in math. Radians is similar to degrees as 360 makes a full round on a coordinate plane, but a radian makes a circumference of a circle and is represented as 2pi. Radians is used in calculus the most because it gives you a more proper answer. Showing the relationship between sin and cosine for example can be very messy if not used in radians. Basically, radians is just a more elegant and classy way of doing math that gives you an easy to understand answer.
To convert degrees to radians is very simple. The formula is degrees x pi/180.
An example would be 150degrees. -To convert this to radians, you put 150 x pi/180. -You end up with 150pi/180 -Now you simplify. The answer in radians is 6pi/5
It is very simple to convert degrees to radians and it is just as simple to convert radians to degrees. The formula for that is radians x 180/pi.
Radians play a very important role in mathematics. Radians are usually just assumed to be there with the symbol of pi. It is similar to degrees when 360 makes a complete circle around a plane. The circumference is expressed as 2pi. Radians is mostly used to show the relationship between sin and cosine.
To convert from radians to degrees you use the simple formula x180/pi Example: 9pi you would take 9pi and multiply it by pi/180. 9pi/4 x 180/pi the pi's cancel out and your left with 9/4 x 180 multiply 9 x 180 and you get 1620. divide 1620 by 4 your answer is 405 degrees.
Example 2: 3pi/2 3pi/2 x 180/pi pi's cancel out and your left with 3/2 x 180 multiply 3 x 180 and you get 540 divide 540 by 2 your answer is 270 degrees.
A radian is a standard unit of angular measure. It is used in many mathematics areas. It is represented as “rad”. Another way to identify the radians symbol is by the superscript which is the circular measure. Some mathematical writing the symbol “rad” is almost always omitted. A radian makes a circumference of a circle and it is represented as 2π.
Converting degrees to radians is very easy. The formula you use to convert degrees to radians is x π/180.
Examples: Converting degrees to radians.
• 200 degrees o First you do 200 x π/180. o You end up getting 200π/180. o Now you simplify. o You get 10π/9.
• 300 degrees o First you do 300 x π/180. o You end up getting 300π/180. o Now you simplify. o You get 5π/3.
Converting radians to degrees is easy also. The formula you use to convert degrees to radians is radians x 180/π.
Examples: Converting radians to degrees
• 4π. o First the π gets canceled. o You end up with 4/1 x 180/1. o You get 720 degrees.
• 2π. o First the π gets canceled. o You end up with 2/1 x 180/1. o You get 360 degrees.
Basically radian plays a big roll in mathematics and it easier to work with all the time. Examples: calculus, or other branches of government. Radians are the easiest thing to work with than degrees.
In mathematics, radians are not only used in trigonometry but in other areas of math as well. A radian or is the standard unit of angular measure. One radian is represented as the angle subtended at the middle of a circle. The arc in the middle of the circle is equal to the length of the circle’s radius. Radians are a lot like degrees because 360° makes a full circle on a coordinate plane. When it is in radians it is written as 2π.
When converting radians to degrees you use this formula: radian x 180/π
Example 1:
4π/2 x 180/π = 360
1) When you multiply the 2 together the π’s cancel.
2) Then you multiply 4 x 180 and get 720
3) Divide by 2 to get your answer of 360°
When converting degrees to radians you use this formula: ° x π/180
Example 2:
540° x π/180 = 3π
1) Multiply to get 540π/180 2) Divide to get your answer of 3π
Radians are a unit of measurement in math. Radians are similar to degrees. For example: 360 degrees- 2pi, 270degrees=3pi/2, 180degrees=pi, and 90degrees=pi/2 on a coordinate plane. The circumference of a whole circle it is 2pi in radians. In calculus, radians are used more often to illustrate a more proper answer. When not showed in radians, the relationship between sine and cosine can become messy and confusing. In all reality, radians are just a better way to show your answer. It is easier to understand, more precise, and neater.
To convert degrees to radians is very simple. The formula is degrees x pi/180. And it is also very simple to convert radians to degrees the formula is degrees x 180/pi.
An example would be 135degrees. -To convert this to radians, you put 135 x pi/180. -You end up with 135pi/180 -Now you simplify. The answer in radians is 3pi/4
One radian is the angle of an arc created by wrapping the radius of a circle around its circumference.
In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside:
The radius 'r' fits around the circumference of a circle exactly 2p times. That is why the circumference of a circle is given by:
circumference = 2pr
So there are 2p radians in a complete circle, and p radians in a half circle.
Converting radians to degrees:
To convert radians to degrees, we make use of the fact that p radians equals one half circle, or 180º.
This means that if we divide radians by p, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees.
So, to convert radians to degrees, multiply by 180/p, like this:
The radian is the standard unit of angular measure, used in many areas of mathematics. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit. The SI unit of solid angle measurement is the steradian.
The radian is represented by the symbol "rad" or, more rarely, by the superscript c. For example, an angle of 1.2 radians would be written as "1.2 rad" or "1.2c" . As the ratio of two lengths, the radian is a "pure number" that needs no unit symbol, and in mathematical writing the symbol "rad" is almost always omitted. In the absence of any symbol radians are assumed, and when degrees are meant the symbol ° is used
Converting radians to degrees and converting degrees to radians is a very simple process to do.
To convert degrees to radians you multiply by pi/180.
To convert radians to degrees you multiply by 180/pi.
Ex. 3pi the pi's cancel and you gt 3 x 180 which equals 540
A radian is a unit of measurement defined as 180/π°, or roughly 57.2958°. Sometimes abbreviated as rad or as the subscript c, standing for "circular measure," the radian is the standard unit of measurement for angles in mathematics. The radian was first conceived of by English mathematician Roger Cotes in 1714, though he did not name the unit of measurement. The word radian first appeared in print in 1873.
I find a radian important because to be able to graph you will not always need a degree but a radian. Radians are preferred to other units of angle measurement, such as degrees and grads, because of their naturalness, or their ability to produce elegant and simple results, particularly in the field of trigonometry.
To convert radians you must multiply by 180/π in order to get the answer. For example:
8π/2 in order to get it to radians you multiply by 180/π 8π/2*180/π
Pi's cancel and you get 1440/2 which simplifies to: 270°
The arc in the middle of the circle is equal to the length of the circle’s radius. Radians are a lot like degrees because 360° makes a full circle on a coordinate plane. When it is in radians it is written as 2π. In math, radians are not only used in trigonometry but in other areas of math as well. A radian or is the standard unit of angular measure. One radian is represented as the angle subtended at the middle of a circle. Showing the relationship between sin and cosine for example can be very messy if not used in radians. When converting radians to degrees you use this formula: radian x 180/π
Ex. 4π/2 x 180/π = 360 When you multiply the 2 together the π’s cancel. Then you multiply 4 x 180 and get 720 Divide by 2 to get your answer of 360° When converting degrees to radians you use this formula: ° x π/180
Radians are the standard unit of angle measurements. Therefore to measure anything else in trig you must use radians as a standard. For example when radians are compared to degrees in trig 2(pi) in radians = 360 degrees, 3(pi)/2= 270 degrees, (pi)= 180 degrees, (pi)/2= 90 degrees. In the unit circle pie/2 is located at (0,1), (pie) is located at (-1,0), 3(pie)/2 is located at (0,-1), and 2(pie) is located at (1,0). It is said that one radian is equal to 180/pi. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of a circle.
Degrees can be converted to radians by doing (pie)/180. Radians can be converted back to degrees by doing 180/(pie).
Ex. From degrees to radians 30 * pie/180 = 30(pie)/180 = pie/6 radians
Ex. From radians to degrees pie/6*180/(pie)= 180(pie)/6pie)= 30 degrees
A radian is a figure commonly used in trigonometry. It most normally pertains to circles and in one form can be used to represent 360 degrees. Radians are most commonly represented using pi. 1pi is equal to 180 degrees on the unit circle. Therefore a value of 2pi is equal to 360 degrees. Even though this comes as the full 360 degrees it is not the end. By adding a value of pi to this it will keep going. If you take a value of pi and multiply it by 180 degrees/pi. You will get the degree value of the radian.
Ex.
7pi/8. convert to degrees.
7pi/8 *180/pi. The pis cancel and you are left with 1260/8. The final value is 155 degrees.
A radian is a standard unit of angular measurement and it is used in many areas of mathematics. The radian is represented by the symbol “rad”. In mathematical writing, the unit rad is usually omitted. If there is no symbol, radians are assumed. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2pir /r, or 2pi. Thus 2pi radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees.
ReplyDeleteThere is a way to convert radians to degrees too.. All you do is multiply by 180/pi. Here’s an example..
EXAMPLE 1: pi/6 x 180/pi
A). The pi(s) cancel and you get 180/6 which is 30.
B). Therefore, your answer will be 30 degrees.
EXAMPLE 2: 5pi/3 x 180/pi
A). The pi(s) cancel and you are left with 5/3 x 180/1.
B). Therefore, your answer will be 300 degrees.
Just like you can convert radians to degrees, you can also convert degrees to radians. The formula is degrees x pi/180.
In calculus or other branches of math, angles are universally measured in radians. Why? Because radians have a mathematical “naturalness” that leads to a more elegant formation of a number of important results. Although the radian is a unit of measure, it is a dimensionless quantity. So as you can see, radians are much easier to work with. If you’re working with degrees, you’ll first have to graph it then convert it to radians.
http://en.wikipedia.org/wiki/Radian
This comment has been removed by the author.
ReplyDeleteA radian is a unit of measure in math. Radians is similar to degrees as 360 makes a full round on a coordinate plane, but a radian makes a circumference of a circle and is represented as 2pi. Radians is used in calculus the most because it gives you a more proper answer. Showing the relationship between sin and cosine for example can be very messy if not used in radians. Basically, radians is just a more elegant and classy way of doing math that gives you an easy to understand answer.
ReplyDeleteTo convert degrees to radians is very simple. The formula is degrees x pi/180.
An example would be 150degrees.
-To convert this to radians, you put 150 x pi/180.
-You end up with 150pi/180
-Now you simplify. The answer in radians is 6pi/5
It is very simple to convert degrees to radians and it is just as simple to convert radians to degrees. The formula for that is radians x 180/pi.
http://en.wikipedia.org/wiki/Radian
Radians play a very important role in mathematics. Radians are usually just assumed to be there with the symbol of pi. It is similar to degrees when 360 makes a complete circle around a plane. The circumference is expressed as 2pi. Radians is mostly used to show the relationship between sin and cosine.
ReplyDeleteTo convert from radians to degrees you use the simple formula x180/pi
Example:
9pi
you would take 9pi and multiply it by pi/180.
9pi/4 x 180/pi
the pi's cancel out and your left with 9/4 x 180
multiply 9 x 180 and you get 1620.
divide 1620 by 4
your answer is 405 degrees.
Example 2:
3pi/2
3pi/2 x 180/pi
pi's cancel out and your left with 3/2 x 180
multiply 3 x 180 and you get 540
divide 540 by 2
your answer is 270 degrees.
http://en.wikipedia.org/wiki/Radians
A radian is a standard unit of angular measure. It is used in many mathematics areas. It is represented as “rad”. Another way to identify the radians symbol is by the superscript which is the circular measure. Some mathematical writing the symbol “rad” is almost always omitted. A radian makes a circumference of a circle and it is represented as 2π.
ReplyDeleteConverting degrees to radians is very easy. The formula you use to convert degrees to radians is x π/180.
Examples: Converting degrees to radians.
• 200 degrees
o First you do 200 x π/180.
o You end up getting 200π/180.
o Now you simplify.
o You get 10π/9.
• 300 degrees
o First you do 300 x π/180.
o You end up getting 300π/180.
o Now you simplify.
o You get 5π/3.
Converting radians to degrees is easy also. The formula you use to convert degrees to radians is radians x 180/π.
Examples: Converting radians to degrees
• 4π.
o First the π gets canceled.
o You end up with 4/1 x 180/1.
o You get 720 degrees.
• 2π.
o First the π gets canceled.
o You end up with 2/1 x 180/1.
o You get 360 degrees.
Basically radian plays a big roll in mathematics and it easier to work with all the time. Examples: calculus, or other branches of government. Radians are the easiest thing to work with than degrees.
http://en.wikipedia.org/wiki/Radian
In mathematics, radians are not only used in trigonometry but in other areas of math as well. A radian or is the standard unit of angular measure. One radian is represented as the angle subtended at the middle of a circle. The arc in the middle of the circle is equal to the length of the circle’s radius. Radians are a lot like degrees because 360° makes a full circle on a coordinate plane. When it is in radians it is written as 2π.
ReplyDeleteWhen converting radians to degrees you use this formula: radian x 180/π
Example 1:
4π/2 x 180/π = 360
1) When you multiply the 2 together the π’s cancel.
2) Then you multiply 4 x 180 and get 720
3) Divide by 2 to get your answer of 360°
When converting degrees to radians you use this formula: ° x π/180
Example 2:
540° x π/180 = 3π
1) Multiply to get 540π/180
2) Divide to get your answer of 3π
http://en.wikipedia.org/wiki/Radian
Radians are a unit of measurement in math. Radians are similar to degrees. For example: 360 degrees- 2pi, 270degrees=3pi/2, 180degrees=pi, and 90degrees=pi/2 on a coordinate plane. The circumference of a whole circle it is 2pi in radians. In calculus, radians are used more often to illustrate a more proper answer. When not showed in radians, the relationship between sine and cosine can become messy and confusing. In all reality, radians are just a better way to show your answer. It is easier to understand, more precise, and neater.
ReplyDeleteTo convert degrees to radians is very simple. The formula is degrees x pi/180.
And it is also very simple to convert radians to degrees the formula is degrees x 180/pi.
An example would be 135degrees.
-To convert this to radians, you put 135 x pi/180.
-You end up with 135pi/180
-Now you simplify. The answer in radians is 3pi/4
http://en.wikipedia.org/wiki/Radian
What are 'radians' ?
ReplyDeleteOne radian is the angle of an arc created by wrapping the radius of a circle around its circumference.
In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside:
The radius 'r' fits around the circumference of a circle exactly 2p times. That is why the circumference of a circle is given by:
circumference = 2pr
So there are 2p radians in a complete circle, and p radians in a half circle.
Converting radians to degrees:
To convert radians to degrees, we make use of the fact that p radians equals one half circle, or 180º.
This means that if we divide radians by p, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees.
So, to convert radians to degrees, multiply by 180/p, like this:
http://www.teacherschoice.com.au/maths_library/angles/angles.htm
The radian is the standard unit of angular measure, used in many areas of mathematics. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit. The SI unit of solid angle measurement is the steradian.
ReplyDeleteThe radian is represented by the symbol "rad" or, more rarely, by the superscript c. For example, an angle of 1.2 radians would be written as "1.2 rad" or "1.2c" . As the ratio of two lengths, the radian is a "pure number" that needs no unit symbol, and in mathematical writing the symbol "rad" is almost always omitted. In the absence of any symbol radians are assumed, and when degrees are meant the symbol ° is used
Converting radians to degrees and converting degrees to radians is a very simple process to do.
To convert degrees to radians you multiply by pi/180.
To convert radians to degrees you multiply by 180/pi.
Ex. 3pi
the pi's cancel and you gt 3 x 180
which equals 540
http://en.wikipedia.org/wiki/Radian
A radian is a unit of measurement defined as 180/π°, or roughly 57.2958°. Sometimes abbreviated as rad or as the subscript c, standing for "circular measure," the radian is the standard unit of measurement for angles in mathematics. The radian was first conceived of by English mathematician Roger Cotes in 1714, though he did not name the unit of measurement. The word radian first appeared in print in 1873.
ReplyDeleteI find a radian important because to be able to graph you will not always need a degree but a radian. Radians are preferred to other units of angle measurement, such as degrees and grads, because of their naturalness, or their ability to produce elegant and simple results, particularly in the field of trigonometry.
To convert radians you must multiply by 180/π in order to get the answer. For example:
8π/2 in order to get it to radians you multiply by 180/π
8π/2*180/π
Pi's cancel and you get 1440/2 which simplifies to: 270°
(http://www.wisegeek.com/what-is-a-radian.htm)
The arc in the middle of the circle is equal to the length of the circle’s radius. Radians are a lot like degrees because 360° makes a full circle on a coordinate plane. When it is in radians it is written as 2π. In math, radians are not only used in trigonometry but in other areas of math as well. A radian or is the standard unit of angular measure. One radian is represented as the angle subtended at the middle of a circle. Showing the relationship between sin and cosine for example can be very messy if not used in radians. When converting radians to degrees you use this formula: radian x 180/π
ReplyDeleteEx.
4π/2 x 180/π = 360
When you multiply the 2 together the π’s cancel.
Then you multiply 4 x 180 and get 720
Divide by 2 to get your answer of 360°
When converting degrees to radians you use this formula: ° x π/180
http://en.wikipedia.org/wiki/Radian
This comment has been removed by the author.
ReplyDeleteRadians are the standard unit of angle measurements. Therefore to measure anything else in trig you must use radians as a standard. For example when radians are compared to degrees in trig 2(pi) in radians = 360 degrees, 3(pi)/2= 270 degrees, (pi)= 180 degrees, (pi)/2= 90 degrees. In the unit circle pie/2 is located at (0,1), (pie) is located at (-1,0), 3(pie)/2 is located at (0,-1), and 2(pie) is located at (1,0). It is said that one radian is equal to 180/pi. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of a circle.
ReplyDeleteDegrees can be converted to radians by doing (pie)/180. Radians can be converted back to degrees by doing 180/(pie).
Ex. From degrees to radians
30 * pie/180 = 30(pie)/180 = pie/6 radians
Ex. From radians to degrees
pie/6*180/(pie)= 180(pie)/6pie)= 30 degrees
http://en.wikipedia.org/wiki/Radian
A radian is a figure commonly used in trigonometry. It most normally pertains to circles and in one form can be used to represent 360 degrees. Radians are most commonly represented using pi. 1pi is equal to 180 degrees on the unit circle. Therefore a value of 2pi is equal to 360 degrees. Even though this comes as the full 360 degrees it is not the end. By adding a value of pi to this it will keep going. If you take a value of pi and multiply it by 180 degrees/pi. You will get the degree value of the radian.
ReplyDeleteEx.
7pi/8. convert to degrees.
7pi/8 *180/pi. The pis cancel and you are left with 1260/8. The final value is 155 degrees.