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The unit circle edu 653

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The unit circle edu 653

1. 1.  A unit circle is a circle that has a center at the origin with a radius of one. The equation of a unit circle is x 2 + y 2 = 1. Using radian measure, we can label the points on the unit circle that correspond with the degree measure.
2. 2.  The radian is a unit of plane angle, equal to 180/ π degrees, or about 57.2958 degrees. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level. http://www.reference.com/browse/Radian
3. 3.  Multiply the degree by π/180 and simplify but leave it in π form. Example    150  15  5150       180  180 18 6
4. 4.  Multiply the radian by 180/π and simplify until you are left with only a degree measure. Example 5  180  900     300  3    3
5. 5.  0º = 0  90º = π/2  180º = π  270º = 3π/2  360º = 2πPicture made by Sarah Allen
6. 6. Picture made by Sarah Allen
7. 7.  Using the special right triangles, we can start to build the points on the circle.Picture made by Sarah Allen
8. 8.  We now know that a 30º angle has a x value of square root of three divided by two and a y value at one half. We can now convert degrees to radian and complete that point on the circle.    30  3  30       180  180 18 6
9. 9. Based on our results,we found that at π/6we have the pointsquare root of threedivided by two andone half. We cancontinue this aroundentire unit circle,which is explained inthe video on thenext slide.Picture made by Sarah Allen
10. 10. Melodyeducate (2011, Feb 8) Building The Unit Circle. Retrieved October 29, 2012 from http://www.youtube.com/watch?v=BXLxl6YRvdc
11. 11.  Now that we know how to built the unit circle we can begin to understand what it was built for.   3 1We know that has the point  ,  6  2 2  and can use this to find both sine and cosine.
12. 12.  Cos = adj/hyp and in the unit circle that is x/1 which is just x Sin = opp/hyp and in the unit circle that is y/1 which is just yThereforecos = x and sin = y and any point on the unit circle can be seen as ( cos, sin )
13. 13. Therefore…   3   1cos    and sin    6 2 6 2
14. 14.  There is a game for the unit circle that can be used for helping in the memorization of the unit circle information. Go to the following link to use this game to help you remember the information you just learned. Click on the unit circle in the lower right hand corner to follow the link. *must have an internet connection to visit the gameFelliax08. (2007). Unit circle. Retrieved October 29, 2012 from http://www.purposegames.com/game/unit-circle-quiz/info Picture made by Sarah Allen
15. 15. 1. Convert 50º into radian.2. Convert 5π/7 into degree.3. What is the sin (π/3)?4. What is the cos (5π/6)?5. What is the coordinate point of 5π/4 Write your answers onto a sheet of paper and turn in to Mrs. Allen by tomorrow.