Introduction to the Six Trigonometric Functions & the Unit Circle 1.2 Introduction to the Six Trigonometric Functions & the Unit Circle

(0,1)  (-1,0)  (1,0)  (0,-1)

 (?,?) (1,0)  = = 2 (0,1) 1 1 1 y x 2 (-1,0)  x 2 x = 2 (0,-1) 45 1 2 (0,1)  (?,?) 1 y = 1 2 x (-1,0)  (1,0) x x = 2 2  (0,-1) = 1 2 y y = 2 2

   (1,0)    (0,1) (-2/2, 2/2) (2/2, 2/2) (-1,0)  (-2/2, -2/2) (2/2, -2/2)  (0,-1)

  (?,?) (1,0)  = = 3 1 2 (0,1) 1 y 1 2 x (-1,0)  x x = 1 2 60 30 3 1 2 (0,1)   (?,?) 1 y = 1 2 x (-1,0)  (1,0) x x = 1 2  (0,-1) y 3 1 2 = y = 3 2

     (1,0)      (0,1) (-1/2, 3/2) (1/2, 3/2) (-2/2, 2/2) (2/2, 2/2)   (-1,0)  (1,0)   (-2/2, -2/2)  (2/2, -2/2)  (-1/2, -3/2)  (1/2, -3/2) (0,-1)

  (?,?) (1,0)  = = 1 2 3 (0,1) x 3 1 2 1 y (-1,0)  x = 3 2 x 60 30 1 2 3 (0,1)  x 3 1 2 =  (?,?) 1 y (-1,0)  (1,0) x = 3 2 x  (0,-1) = 1 2 y y = 1 2

       (1,0)        (0,1) (-1/2, 3/2) (1/2, 3/2) (-2/2, 2/2) (2/2, 2/2)   (-3/2, 1/2) (3/2, 1/2)   (-1,0)  (1,0)   (-3/2, -1/2) (3/2, -1/2)   (-2/2, -2/2)  (2/2, -2/2)  (-1/2, -3/2)  (1/2, -3/2) (0,-1)

The six trigonometric functions… Sine – sin Cosine – cos Tangent – tan Cosecant – csc Secant – sec Cotangent - cot

Unit Circle Definitions of the 6 Trig. Functions… csc = 1 y sin = y sec = 1 x cos = x cot = x y tan = y x

Practice: Determine the exact value of each without the aid of a calculator. sin =  3 cos = 5 6 tan = 3 2 csc =  sec =  2 cot = 4 3

Practice: Determine the exact value of each without the aid of a calculator. sin 120= cos 300 = tan 45= csc 90= sec 210= cot 0=

Practice: Determine the exact value of each without the aid of a calculator. sin 405= cos 540 = tan (-300)= csc (-120)= sec 855= cot 945=

Practice: Determine the exact value of each without the aid of a calculator. sin = 19 6 cos = 5 Tan = -2 3 csc = 11 4 sec = 9 2 cot = -8 3

Using the Calculator to Evaluate the 6 Trig. Functions… sin 212= sin (212)= -.5299 cos 319= cos (319)= .7547 tan (-402)= tan (-402)= -.9004 Be sure your calculator is set in Degree Mode…or you will get an incorrect answer.

Using the Calculator to Evaluate the 6 Trig. Functions… sin /8= sin (/8)= .3827 cos 5/7 = cos (5/7 )= -.6235 tan (- 2/9 )= tan (- 2/9 )= -.8391 Be sure your calculator is set in Radian Mode…or you will get an incorrect answer.

What if there is no calculator button?.... csc 48= sin (48)= .7431 x-1 =1.3456 Since it is the reciprocal of the sin…use the sin button then reciprocate it… x-1 sec 153= cos (153)= -.8910 x-1 =-1.1223 =-.2679 cot (-75)= tan (-75)= -3.7321 x-1