7-1/ Degrees and Radians

So I'm going to be explaining a few different things. The first thing is how to break down degrees into minutes and seconds. The others are how to convert degrees into radians and converting radians into degrees.

*Breaking down degrees into minutes and seconds have 2 easy steps:

1. The first thing you want to do is convert the degree they give you into minutes. To do this you would take what is behind the decimal of the degree and multiply it by 60.
2. The next step is to then convert to seconds. Would would then take what is behind the decimal of the minutes and mulitply by 60.

NOTE: The only time you would ever break down a degree into minutes and seconds would be when the degree they give you has a decimal. The point of breaking it down is to get a number that isn't a decimal.

**Now we are going to convert degrees into radians. You can do this in one simple step.

1. The formula for converting degrees into radians is: degrees X Pi/180=radian. This formula is very simple. If you were using a calculator you would plug in the degrees and divide it by 180. You would then convert that answer into fraction form and put the pi symbol besides it.

***I am now going to tell you how to convert radians back into degrees. You can do this in one simple step too.

1. The formula for converting radians back into degrees is: radian X 180/Pi=degree. This formula is once again very simple. If your radian has a Pi symbol, then they were cancel each other out and you would simply divide the radian by 180. If your radian doesn't have a Pi symbol, then you would still divide the radian by 180 but now you would just add the Pi symbol to the side of your answer.

NOTE: Not all radians have Pi symbols, this is why it is very important to know that degrees will always have the degree symbol. You need to know that to be able to tell radians and degrees apart.

Okay, so now I am going to give you an example of each of the problems I explained above. Note that I am going to use the star symbols on side of each new problem so you know which one I am working. I am also going to number each step I do to match the ones above.

*Example 1: Break down the degree given into minutes and seconds.

14.21 degrees

1. .21 x 60= 12.6
2. .6 x 60= 36

Your answer would then be: 14 degrees 12 minutes and 36 seconds.

**Example 2: Convert the degree given into a radian.

315 degrees

1. 315 x Pi/180= 7/4 Pi

Your answer would then be: 7/4 Pi

***Example 3: Convert the radian given into a degree.

4 Pi/3

1. 4 Pi/3 x 180/Pi= 240 degrees

Your answer would then be: 240 degrees.

And that is pretty much it!

--Halie :)