1. Chapter 4 Trigonometric Functions
Section 4.1 Angles and Their Measures

2. Homework
Section 4.1 Exercises #17-38, 53, 54

3. The circumference of a circle is 𝐶=2𝜋𝑟 and where 𝑟=1, 𝐶=2𝜋.
The Problem of 360 𝑜 If told that you walked exactly 12 𝑜 , how far did you go? Consider a circle who has a radius of any one unit.
The circumference of a circle is 𝐶=2𝜋𝑟 and where 𝑟=1, 𝐶=2𝜋.
Therefore 360 𝑜 =2𝜋 or 𝜋= 180 𝑜 .
This conversion provides the basis for a linear system of measurements known as radians (abbrv. rad).
𝑟=1

4. 𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠= 180 𝑜 1 𝑟𝑎𝑑𝑖𝑎𝑛=57.30 To convert from degrees to radians multiply by 𝜋 180 𝑜 To convert from radians to degrees multiply by 180 𝑜 𝜋 EX1: Convert each of the following to radians: a. 90 𝑜 90 𝑜 𝜋 180 𝑜 = 𝜋 2 rad b. 30 𝑜 30 𝑜 𝜋 180 𝑜 = 𝜋 6 rad

5. EX2: Convert the following radian measures into degrees a
EX2: Convert the following radian measures into degrees a. 5𝜋 6 rad 5𝜋 𝜋 = 150 𝑜 b rad 𝜋 = 𝑜

6. Arc Length Formula: 𝑠=𝑟𝜃 𝑠 – arc length 𝑟 – radius 𝜃 – central angle in radians EX3: Find the perimeter of a sector whose central angle is 38 𝑜 and radius is 12 meters. 𝑠= 𝜋 180 𝑠= 𝜋 or 𝑠=7.96 meters

7. EX4: The tire on a car has a radius of 20 inches and rotates as a rate of 500 rpm (rotations per minute). Determine the speed of the car in miles per hour. What is one rotation equal to in radians? What is 1 radian equal to in inches? 500𝑟𝑒𝑣 𝑚𝑖𝑛 × 60𝑚𝑖𝑛 ℎ𝑟 × 2𝜋 𝑟𝑎𝑑 1𝑟𝑒𝑣 × 20𝑖𝑛 𝑟𝑎𝑑 × 1𝑓𝑡 12𝑖𝑛 × 1𝑚𝑖 5280𝑓𝑡 ≈59.5 𝑚𝑖𝑙𝑒𝑠 ℎ𝑜𝑢𝑟

8. Homework
Section 4.1 Exercises #17-38, 53, 54