7-1 Degrees and Radians

This section is all about conversions. First we will be converting degrees to minutes and seconds. Then we will be converting degrees to radians and radians to degrees.

1. Converting degrees to minutes and seconds
You only have to convert degrees to minutes(') and seconds(") if it is a decimal.

• When converting to minutes you take what is behind the decimal in the degrees and multiply it by 60. (If you still have a decimal then you have to then convert to seconds)


• When you convert to seconds you take the numbers that are behind the decimal in the minutes and multiply by 60. (If you still have a decimal you just drop of the numbers behind the decimal when you right your answer)

2. Converting degrees to radians

• All you have to do to convert degrees to radians is plug into the formula: degrees * pi/180 (you can do this easily by entering in your calculator, degrees/180, change the answer to a fraction, and put pi on the side of it.

3. Converting radians to degrees

• To convert from radians to degrees, you plug into the formula rads * 180/pi (if the radians have pi in it then pi will cancel each other out)

Examples:

1.Convert 75.63 degrees to minutes and seconds:

.63*60=37.8' .8*60=48"

The final answer is 75 degrees 37' 48"

2. Convert 212 degrees to radians:

212 degrees * pi/180=(53/45) pi

The answer is (53/45) pi

3. Convert (2 pi/3) to degrees:

(2 pi/3)*(180/pi)=((2*180)/3)=(360/3)=120 degrees

The answer would be 120 degrees

-Braxton-