Treeeee

Measurement of a twig from the ground:

80 degrees --- 4π/9 rad

Work Cited

Angle Conversions. TeachersChoice, 2009. Web. 8 Jan. 2012. <http://www.teacherschoice.com.au/maths_library/angles/angles.htm>. 

"Degrees and Radians." YouTube: 1 Dec 2008. Web. 8 Jan 2012. <http://www.youtube.com  /watch?v=cLBKOYmHuDM&feature=player_embedded>. 

PatrickJMT. A Trick to Remember Values on The Unit Circle. 2008. Video. YouTubeWeb. 8 Jan 2012. <http://www.youtube.com/watch?v=ao4EJzNWmK8&feature=player_embedded>. 


 "Unit Circle." Math Is Fun. N.p., 2011. Web. 8 Jan 2012. <http://www.mathsisfun.com/geometry/unit-circle.html>.

Using Paper Plate To Measure Real Life Angles

Here's a branch from a tree in my back yard:

Here, I use the Paper Plate to measure the angle between to branches (Pics aren't accurate because I couldn't take the pic and hold the branch steady with one hand....)

The angle between the two branches is 35°  and  7π/36 rad

Here are two twigs coming up from the ground. (again, pictures aren't accurate measurements and the plate is upside down)

The angle between the two twigs is 75° and 5 π/12

Finding Radians

1. Explain how each degree was converted to radians.

First, I took 180 (which has a corresponding radian of just π) and divided it by 5, because the angles increase by 5 degrees. 1 could have divided the degree (times π) by 180 but you would always have to reduce. 180/5 is equal to 36. This is how I knew that the denominator for every radian would be 36. I then took the degree that I was finding the radian for, and divided that by 5 -- because what is done to one side should be done to the other. The resulting number is the numerator for the fraction. 


Here's an example of my work when finding the radian for 30°:


Step 1: divide 180° by 5 to reduce (360° is double 180° -- and the radians are 2π and π, respectively-- this is why dividing into 360 is unnecessary, because 180 is a easier degree to reduce from)

180°/5° = 36 

Step 2: Divide 30° by 5 because you divided 180 by 5. 

30°/5=6°

Step 3: 36 is the "universal" denominator, because the circle increases by 5 consistently and we are converting all the degrees to radians.

6°/36° 

Step 4: Reduce the fraction and don't forget the numerator is multiplied by π (since we are dealing with a circle) 


6 is common factor of 6 and 36. Finally answer is---> π/6 


This is how all the radian conversions were completed, I also used an online calculator to check all of my conversions.
http://www.mattdoyle.net/old/raddeg.html

 

Finished Plate

Complete plate with 360 degrees and their corresponding radians.

Step 3: Finish up the plate

First step: Label the 73 dimple plate in increments of 5 degrees....

 Keep going....almost there... (I messed up on 5 plates just by skipping 5s)

 

AND THAT'S ALL FOLKS!

NOW: FIGURE OUT HOW TO CONVERT DEGREES TO RADIANS

Here's a YouTube video I found that helped a lot. Plus, the guy sounds smart so....

This website also helped,

It shows the relationship between angles and radians, and how to convert angles to radians and vice versa.
This calculator tool was also a big help when checking my conversions..

Plates Galore :(

I have never counted so many plastic plates in my entire life (and,  like 10 people caught me and gave me the "you're a weirdo" look.  I counted this one plate 6 times, because I kept losing track. Nonetheless, I found it!
Now I have to figure out if I'm labeling the indent or the bump of each "dimple". *sighs*