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Special Right Triangles and the Unit Circle
Special Right Triangles and the Unit Circle February 20, 2009 5.2 Right Triangle Trigonometry opposite hy po te nu se adjacent Objective: Find rectangular points on the unit circle. Feb 1910:24 AM 1 Special Right Triangles and the Unit Circle February 20, 2009 The "BIG 3" functions are defined: opposite hy po ten us e adjacent SOH CAH TOA Feb 1910:25 AM 2 Special Right Triangles and the Unit Circle February 20, 2009 There are three more functions, but they are just reciprocals of the big 3. sine cosecant cosine secant tangent cotangent Feb 1910:25 AM 3 Special Right Triangles and the Unit Circle February 20, 2009 Special Right Triangle Relationships o o 45 30 2 1 2 3 o 45 1 o 60 1 Feb 1910:28 AM 4 Special Right Triangles and the Unit Circle February 20, 2009 o o Fill in the degrees and radians for every multiple of 45 and 30. Feb 193:54 PM 5 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 135 150 30 180 360 210 330 225 315 300 240 270 Feb 1910:29 AM 6 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 135 150 30 180 360 210 330 225 315 300 240 270 Feb 1910:29 AM 7 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 135 150 30 180 360 210 330 225 315 300 240 270 Feb 1910:29 AM 8 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 135 150 30 180 360 210 330 225 315 300 240 270 Feb 1910:29 AM 9 Special Right Triangles and the Unit Circle February 20, 2009 (0, 1 ) 90 120 60 45 135 150 (1, 0 ) 30 180 360 (1, 0 ) 210 330 225 315 300 240 270 (0, 1 ) Feb 1910:58 AM 10 Special Right Triangles and the Unit Circle February 20, 2009 (0, 1 ) 90 ( , + ) 120 ( +, + ) 60 45 135 150 (1, 0 ) 30 180 360 (1, 0 ) 210 330 225 ( , ) 315 300 240 270 ( +, ) (0, 1 ) Feb 1910:58 AM 11 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 135 r 150 180 y 30 360 x 210 330 225 315 300 240 270 Feb 1910:29 AM 12 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 e 135 nus 150 30 hyp ote opposite 180 360 adjacent 210 330 225 315 300 240 270 Feb 1910:29 AM 13 Special Right Triangles and the Unit Circle February 20, 2009 90 120 60 45 r nus 150 e 135 30 ote opposite hyp y 180 360 adjacent x 210 330 225 315 300 240 270 Feb 1910:29 AM 14 Special Right Triangles and the Unit Circle February 20, 2009 90 120 y sin = r 60 45 r nus 150 e 135 ote 30 opposite hyp y 180 360 adjacent x 210 330 225 315 300 240 x cos = r y tan = x 270 Feb 1910:29 AM 15 Special Right Triangles and the Unit Circle February 20, 2009 5.2 A worksheet #'s: 714, 1535 odds Feb 194:10 PM 16