6.2.1 Trigonometric Functions of Angles
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
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
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
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()
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 = = c = c = 25 = c = 25 = c 2 c = 5 c = 5
Special Triangles 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) =
Special Triangles 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) =
Table of Values of Trigonometric Functions
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
Homework: P odd P odd