Solving for sin using pi
I was messing around with calculating pi by finding the perimeter of a many sided polygon, and dividing it by the diameter (Like the thing Archimedes did). The equation I found was
n(sin(180/n))=pi, where n is the number of sides the polygon has. I was wondering if there was any way to reverse this equation, making it so that you can solve for sine using pi.
Here is what I tried:
(Note: This is all in degrees because I do not know radians that well)
This is what I started with
Divide both sides by
180/n to get
Then I multiplied both sides of that by
n to get
And divided both sides by a to get
Now I have solved that equation for
n, so I can substitute it back into my original equation
n to get
(sin(a))=pi/(180/a), which can be
sin(a)=pi*a/180. What this says is that the
sin(a) is equal to
pi*a/180, which definitely isn't true. One interesting thing about this
equation is that it is the equation to convert degrees into radians. Also, if you graph it, you will is very close to the sin wave until about 25.
(If you graph this equation, make sure you are using degrees and not radians)
After trying this out, I did some reasearch and found there is no easy way to calculate sine. However, I would still like to know what was wrong with the math I did to simplify this.
I am 13 and this is my first question I have posted, so please excuse any mistakes.