Converting angles in to degree to angles in radians

[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?

 

[ideasrule]

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.

 

[berkeman]

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.