THE UNIT CIRCLE Initially Developed by LZHS Advanced Math Team (Keith Bullion, Katie Nerroth, Bryan Stortz) Edited and Modified by Jeff Bivin Lake Zurich High School Jeff Bivin -- LZHS

2s s 30 o 90 o 60 o if 2s = 1 s = ½ Jeff Bivin -- LZHS

30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 150 o Jeff Bivin -- LZHS

30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 210 o Jeff Bivin -- LZHS

30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 330 o Jeff Bivin -- LZHS

60 o 90 o 30 o s 2s if 2s = 1 s = ½ Jeff Bivin -- LZHS

60 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o Jeff Bivin -- LZHS

90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 60 o 120 o Jeff Bivin -- LZHS

90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 240 o 60 o Jeff Bivin -- LZHS

90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 300 o 60 o Jeff Bivin -- LZHS

45 o 90 o s s if Jeff Bivin -- LZHS

45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 135 o Jeff Bivin -- LZHS

45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 225 o Jeff Bivin -- LZHS

45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 315 o Jeff Bivin -- LZHS

2x x 30 o 90 o 60 o 90 o 30 o x 2x 45 o 90 o x x (1, 0) (-1, 0) (0, 1) (0, -1) Putting it Together Jeff Bivin -- LZHS

, (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

, (1, 0) (-1, 0) (0, 1) (0, -1) Walking around by 30 o Jeff Bivin -- LZHS

, (1, 0) (-1, 0) (0, 1) (0, -1) Walking around by 45 o Jeff Bivin -- LZHS

, (1, 0) (-1, 0) Walking around by 60 o Jeff Bivin -- LZHS

, (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

0 Divide each semi-circle into 4 parts. Jeff Bivin -- LZHS

0 Can we reduce any of those fractions? Divide each semi-circle into 6 parts. Jeff Bivin -- LZHS

0 Putting the radian measures together! Jeff Bivin -- LZHS

0 Compare to the degree measure  π = 180 o Jeff Bivin -- LZHS

0 (1, 0) (-1, 0) (0, 1) (0, -1) Look at the points! Jeff Bivin -- LZHS

, (1, 0) (0, 1) (-1, 0) (0, -1) Putting it all together! Jeff Bivin -- LZHS