1. 6.2.1 Trigonometric Functions of Angles

2. Right Triangle Trigonometry a/b a/b b/c b/c c/a c/a a/c a/c b/a b/a c/b c/b Depends only on  Depends only on 

3. The ratios sin() = b/c reciprocal (1/sin())  sin() = b/c reciprocal (1/sin())  csc() = c/b csc() = c/b cos() = a/c reciprocal (1/cos())  cos() = a/c reciprocal (1/cos())  sec() = c/a sec() = c/a tan() = a/b reciprocal (1/tan())  tan() = a/b reciprocal (1/tan())  cot() = b/a cot() = b/a

4. Soh, Cah, Toa Soh  sin = opposite/hypotenuse Soh  sin = opposite/hypotenuse Cah  cos = adjacent/hypotenuse Cah  cos = adjacent/hypotenuse Toa  tan = opposite/adjacent Toa  tan = opposite/adjacent sin() = b/c sin() = b/c cos() = a/c cos() = a/c tan() = a/b tan() = a/b

5. Reciprocal Identites As you can see previously As you can see previously sin() = b/c reciprocal (1/sin())  sin() = b/c reciprocal (1/sin())  csc() = c/b csc() = c/b This is called a Reciprocal Identities (3) This is called a Reciprocal Identities (3) sin() = 1/ csc() sin() = 1/ csc() cos() = 1/ sec() cos() = 1/ sec() tan() = 1/ cot() tan() = 1/ cot()

6. Recall: Pythagorean Theorem a 2 + b 2 = c 2 a 2 + b 2 = c 2 Ex.1) Ex.1) Find a,b, and c given Find a,b, and c given tan() = ¾ tan() = ¾ tan() = b/a tan() = b/a b = 3 b = 3 a = 4 a = 4 4 2 + 3 2 = c 2 4 2 + 3 2 = c 2 16 + 9 = 25 = c 2 16 + 9 = 25 = c 2 c = 5 c = 5

7. Special Triangles 30-60-90 30-60-90 Find the Ratios: Find the Ratios: Sin(60) = Sin(60) = Cos(60) = Cos(60) = Tan(60) = Tan(60) = Sin(30) = Sin(30) = Cos(30) = Cos(30) = Tan (30) = Tan (30) =

8. Special Triangles 45-45-90 45-45-90 Find the Ratios: Find the Ratios: Sin(45) = Cos(45) = Sin(45) = Cos(45) = Csc(45) = Sec (45) = Csc(45) = Sec (45) = Tan(45) = Cot(45) = Tan(45) = Cot(45) =

9. Table of Values of Trigonometric Functions

10. Height of a Vertical Object Given: Given: Surveyor at point A 30’ away from base B Surveyor at point A 30’ away from base B The angle from top of building to surveyor is 30 The angle from top of building to surveyor is 30 Approximate the height of the building Approximate the height of the building B h A 30  30’ Vertical Object

11. Homework: P. 417 1-23 odd P. 417 1-23 odd