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# Copy of The Unit Circle

This Prezi is a response to homework given by my Pre-Calculus teacher involving dividing the unit circle in terms of pi.

by Flavius Marcon
on 9 January 2013
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#### Transcript of Copy of The Unit Circle

Finally Well that's the unit circle. No matter how many people are sharing the pizza, you can use the same method. Need 12 slices? Use 12 arcs. So... Mr. Poliquin gives a problem. The Unit Circle Problem 1

-Graph the unit circle and subdivide it into eight arcs of equal length such that one division lies at the point (1,0)

-Working in a counter-clockwise direction, determine the distance along the unit circle from point (1,0) to each of the divisions, and label each division with this distance Don't Panic!!! I see you freaking out over there. But don't worry, I know we can solve this. Just take it one step at a time (or one arc at a time?). Just read carefully and do what it says. Step 2 What's this arc business? Well, just think of pizza. Eight equal slices, eight equal arcs. Step 1 The problem says "Graph the unit circle...". Okay, so what's that? Step 3 OK, so far so good. So how big are those arcs anyway? How far are they from point (1,0)? ...and where we get it from. You have 10 seconds... go. I took a quick trip to Wikipedia, and the first thing it said was blah blah a unit circle is a circle with a radius of one blah blah blah... Ok, easy enough. Boom. Graphed. 1 1 -1 -1 1 2 3 4 5 6 7 8 arc radius (1,0) So a circle has 360 degrees right? Well 360/8=45. So in relation to (1,0)... 45º 90º 135º 180º 225º 270º 315º 360º counter-clockwise But what are the actual arc measures? Well, the circumference is πd. We have 8 arcs. So any one arc is πd/8. The diameter of the unit circle is 2, so each arc measures π/4. Following our counter-clockwise pattern, the distance from home base aka (1,0) would be 1π/4, 2π/4 (which simplified is π/2), and so on every 45º, all the way up to 8π/4, or 2π ( the whole 360º circumference). That looks like this... π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π

See the full transcript-Graph the unit circle and subdivide it into eight arcs of equal length such that one division lies at the point (1,0)

-Working in a counter-clockwise direction, determine the distance along the unit circle from point (1,0) to each of the divisions, and label each division with this distance Don't Panic!!! I see you freaking out over there. But don't worry, I know we can solve this. Just take it one step at a time (or one arc at a time?). Just read carefully and do what it says. Step 2 What's this arc business? Well, just think of pizza. Eight equal slices, eight equal arcs. Step 1 The problem says "Graph the unit circle...". Okay, so what's that? Step 3 OK, so far so good. So how big are those arcs anyway? How far are they from point (1,0)? ...and where we get it from. You have 10 seconds... go. I took a quick trip to Wikipedia, and the first thing it said was blah blah a unit circle is a circle with a radius of one blah blah blah... Ok, easy enough. Boom. Graphed. 1 1 -1 -1 1 2 3 4 5 6 7 8 arc radius (1,0) So a circle has 360 degrees right? Well 360/8=45. So in relation to (1,0)... 45º 90º 135º 180º 225º 270º 315º 360º counter-clockwise But what are the actual arc measures? Well, the circumference is πd. We have 8 arcs. So any one arc is πd/8. The diameter of the unit circle is 2, so each arc measures π/4. Following our counter-clockwise pattern, the distance from home base aka (1,0) would be 1π/4, 2π/4 (which simplified is π/2), and so on every 45º, all the way up to 8π/4, or 2π ( the whole 360º circumference). That looks like this... π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π