James Nixon
Topic: π and degree conversion
11 th Grade March 9, 2010

f(x) = k(x+a) 2 + c f f(x) = -gt2 + v o x + h o v(x) = mx + b

r
Fully define and explain how it is derived.
Define the unit circle
Understand where the multiple values of π/2, π/3, π/4, and π/6 lie on the unit circle
How to convert from degrees to radian

180
₀
If we want to find out what some angle θ in radian.
Then what we want to know is what ration of 180
₀ and θ is equivalent to some ration of π and the radian measure.
OR
IF θ = 30
₀
Then x or the radian measure = π/6
IF θ = 45
₀
Then x or the radian measure =
IF θ = 60
₀ x = π/3 IF θ = 90
₀ x =
π/4
π/2
This site will show the whole circle filled in, and a graphical representation of Pythagorean Theorem

Unit Circle is a circle with the radius r = 1
Now we can define π or
Learn the history of π

We know that π = 3.1415926…. But why?
And on the previous slides we defined π = 180
₀
π is a ration of the radius of the unit circle to the length of the circumference through 180
₀

Since π is a ration of the radius of the unit circle to the length of the circumference through 180
₀
2 * r = 2
3 * r = 3 r =1
.14159
r = 1
It takes 3.14159… times to wrap the radius r around the circle or 180
₀
.
When r = 1 then rotating 180
₀
= π
If you don’t have the power point to follow along to the links here is the address.
http://www.youtube.com/watch?v=Qq7VV9OYuYE

On the previous sides we converted θ into radians, now lets see where they lie on the unit circle.
2π/3
5π/6
3π/4
135
150
₀
₀
90
120
₀
₀
π/2
60
₀
45
₀
30
₀
π/3
π/4
π/6
180
₀
π
What if you went another 30
₀
45
₀
, 60
₀
, and 90
₀
,
This site will show the whole circle filled in, and a graphical representation of Pythagorean Theorem
With a beginning incite on trig functions.

• How to convert degrees into radian
• Unit Circle defined
• Defined π
Something to think about for extra credit
Using the formula below that was used to find radians,
I want you to rewrite the equation so it uses the radius r and will calculate the arc length of any circle with any given radius.
SHOW YOUR WORK!
HINT: C = 2 π r
C = Circumference
Visual look at the EXTRA CREDIT