# Converting angles in to degree to angles in radians

• tomsdubs
In summary, to convert degrees to radians, you can use the method of multiplying by "1" and using the fraction 2pi radians/360 degrees. This will allow you to convert any angle in degrees to radians by multiplying it by the fraction and canceling out any units. To convert radians to degrees, you would flip the fraction and do the same process. Carrying units along in calculations is an important trick to remember.
tomsdubs

## Homework Statement

Convert the following angles in degree to angles in radians:

15° 60° 80°

## Homework Equations

Now i know that 2 ti c = 360°

And that 6.28 c = 360°

## The Attempt at a Solution

I just can't quite get my head around it, what calculation should i be doing?

2*pi*c=360 degrees, so c=360/(2pi)=180/pi, which is the number of degrees in a radian. So if there are 180/pi degrees per radian, there are 15 degrees per _____ radians.

tomsdubs said:

## Homework Statement

Convert the following angles in degree to angles in radians:

15° 60° 80°

## Homework Equations

Now i know that 2 ti c = 360°

And that 6.28 c = 360°

## The Attempt at a Solution

I just can't quite get my head around it, what calculation should i be doing?

For any units conversions, I like to use the method of multiplying by "1".

The trick is to figure out the best form of "1", and be sure to carry units along with the calculations, cancelling units as appropriate.

So the "1" I would use for these converstions, from degrees to radians, would be:

$$1 = \frac{2 \pi radians}{360 degrees}$$

Then all you have to do to get an angle in radians from an angle in degrees, is to multiply the number by the "1" above, and cancel out any units that are on both top and bottom.

If you were changing units the other way, do you see how you would flip the fraction to do it?

Carrying units along in calculations was a huge trick that I luckily learned early in my first year at university.

## What is the formula for converting angles from degrees to radians?

The formula for converting angles from degrees to radians is: radians = degrees * (π/180).

## Can angles be measured in both degrees and radians?

Yes, angles can be measured in both degrees and radians. Degrees are commonly used in everyday life, while radians are often used in advanced math and science fields.

## How do I convert an angle measured in radians to degrees?

To convert an angle measured in radians to degrees, use the formula: degrees = radians * (180/π).

## What is the relationship between degrees and radians?

Degrees and radians are two different units for measuring angles. One degree is equal to 0.0174533 radians, and one radian is equal to 57.2958 degrees. They are related by the formula: radians = degrees * (π/180).

## Why do we need to convert angles from degrees to radians?

In some mathematical and scientific calculations, it is more convenient to work with angles in radians rather than degrees. Radians are often used in calculus, physics, and engineering because they make certain calculations simpler.

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