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

Relating Knowledge

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

New Vocabulary

Vocabulary Fully define and explain how it is derived. r 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

Degree Radian Conversion 180 ₀ = π 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 =IF θ = 90 ₀ x = π/4 π/3π/2 This site will show the whole circle filled in, and a graphical representation of Pythagorean Theorem

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

Defining π We know that π = …. 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 Back to the Unit Circle

Defining π Since π is a ration of the radius of the unit circle to the length of the circumference through 180 ₀ r =1 2 * r = 2 3 * r = It takes … times to wrap the radius r around the circle or 180 ₀. When r = 1 then rotating 180 ₀ = π r = 1 If you don’t have the power point to follow along to the links here is the address.

Putting it together On the previous sides we converted θ into radians, now lets see where they lie on the unit circle. 30 ₀ 45 ₀ 60 ₀ 90 ₀ π/6 π/4 π/3 π/2 What if you went another 30 ₀, 45 ₀, 60 ₀, and 90 ₀ 135 ₀ 150 ₀ 120 ₀ 180 ₀ 3π/4 5π/6 π 2π/3 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 CREDITEXTRA CREDIT