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Copy of The Unit Circle
Transcript of Copy of The Unit Circle
-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