Radians, Degrees and You...

I'd like to invite the lovers of circles to read this blog. Today, our class was taught about radians and how we can use them along with degrees to confuse us about circles even further than what was already possible.

A radian is another way to measure all the angles in a circle. When the arc of a circle has the same length as the radius, the central angle that intercepts the arc is measured as 1 radian. 

You can find the arc length of a circle with this equation: a=ϴr

     a is arc length

     ϴ is the angle in radians

     r is the radius

THIS IS THE ONE GOLDEN RULE OF LIFE:

     To convert radians to degrees, multiply the radian measure by 180˚/π

     To convert degrees to radians, multiply the degree measure by π/180˚

Example 1.

Degree measure: 360˚

-To find the radian measure of 360˚, you need to convert it using the equation that was literally just stated as the one golden rule of life. (Remember to simplify, children)

360˚(π/180˚)= 360π/180= 2π                   2π is our answer in EXACT radians

                                                                 6.28 is our APPROXIMATE radian measure

Example 2.

Radian measure: π/3

-To find the degree measure, you must (again) use our golden equation.

π/3(180˚/π)=180/3=60˚                           60˚is our answer in degrees

Now that you have a general idea of how to convert radians to degrees, the clock in Mr.Piatek's room should be easier to read than a childrens book. (I know this isn't his clock, but I am not spending more than 10 minutes on google looking for an exact replica)

FRACTIONS ARE PRETTIER THAN DECIMALS

Once you figure out the angles of what each radians represents, I'm sure you have now realized that the order of the radians represents the angles on a circle instead of the time. (Unless you're lazy and read ahead...shame on you) As I'm sure you've noticed, π alone is equal to 180˚ and 2π is 360˚. because the number we've all come to love (3.14159) is actually an approximation, it can only be so accurate, this is why we like to leave our radians as fractions.

I would like to conclude this post on radians, degrees and you by wishing all my fellow pre-calculus students a successful provincial exam and a great year. I hope my post was helpful as a review/teaching tool to those of you reading this. Good luck and math on.