Lesson 1.2 Definition of Trig Functions: Let t be a real number and - - PowerPoint PPT Presentation

Trig Functions: The Unit Circle Lesson 1.2

Definition of Trig Functions: Let t be a real number and let (x, y) be the point on the unit circle corresponding to t. (sine) sin t = y (cosine) cos t = x (tangent) tan t = y/x, x  0

Ex 1: Find the point (x, y) on the unit circle that corresponds to the real number t.

• A. t = /4
• B. t = 7/6
• C. t = 4/3

Ex 2: Evaluate (if possible) the sine, cosine, and tangent of the real number.

• A. t = /4

sin (/4) = cos (/4) = tan (/4) =

2 2 2 2 2 2 2 2

1

2 2 , 2 2 − 3 2 , − 1 2 − 1 2 , − 3 2

Ex 2 (cont’d): Evaluate (if possible) the sine, cosine, and tangent of the real number.

• B. t = 

sin () = cos () = tan () =

1

1   0

−1,0

Ex 2 (cont’d): Evaluate (if possible) the sine, cosine, and tangent of the real number.

• C. t = - 4/3

sin (-4/3) = cos (-4/3) = tan (-4/3) =

3 2  1 2 3 2 1 2 

   3 2 2 1   3 1   3

− 1 2 , 3 2

Definition of Reciprocal Trig Functions: Let t be a real number and let (x, y) be the point on the unit circle corresponding to t. (cosecant) csc t = 1/sin t = 1/y, y  0 (secant) sec t = 1/cos t = 1/x, x  0 (cotangent) cot t = 1/tan t = x/y, y  0

Ex 3: Evaluate (if possible) the six trig functions

• f the real number.
• A. t = 3/4

sin (3/4) = csc (3/4) = cos (3/4) = sec (3/4) = tan (3/4) = cot (3/4) =

2 2  2 2

1

2 2 

2

 2 2

  2

1 1   1

− 2 2 , 2 2

Homework: p.147 #6-28 even

• B. t = -/2

Ex 3 (cont’d): Evaluate (if possible) the six trig functions of the real number. sin (-/2) = cos (-/2) = tan (-/2) = csc (-/2) = sec (- /2) = cot (-/2) = 1

1

Undefined

1 1 

 1

1

Undefined

1 

 0

0, −1