Transcript Chapter 3 Exponential, Logistic, and Logarithmic Functions

Chapter 4
Trigonometric Functions
Section 4.1 Angles and Their Measures
Homework
Section 4.1 Exercises #17-38, 53, 54
The Problem of 360𝑜
If told that you walked exactly 12𝑜 , 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.
𝑟=1
Therefore 360𝑜 = 2𝜋 or 𝜋 = 180𝑜 .
This conversion provides the basis for a linear
system of measurements known as radians
(abbrv. rad).
𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 = 180𝑜
1 𝑟𝑎𝑑𝑖𝑎𝑛 = 57.30
To convert from degrees to radians multiply by
To convert from radians to degrees multiply by
EX1: Convert each of the following to radians:
a. 90𝑜
90𝑜
𝜋
180𝑜
𝑜
𝜋
180𝑜
b. 30𝑜
30
𝜋
2
= rad
𝜋
6
= rad
𝜋
180𝑜
180𝑜
𝜋
EX2: Convert the following radian measures into degrees
a.
5𝜋
6
rad
5𝜋 180
6
𝜋
= 150𝑜
b. 15.25 rad
15.25
180
𝜋
= 873.76𝑜
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 38𝑜 and
radius is 12 meters.
𝑠 = 12 38
𝑠=
38
𝜋
15
𝜋
180
or 𝑠 = 7.96 meters
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
×
×
𝑚𝑖𝑙𝑒𝑠
≈ 59.5
ℎ𝑜𝑢𝑟
1𝑓𝑡
12𝑖𝑛
×
1𝑚𝑖
5280𝑓𝑡
Homework
Section 4.1 Exercises #17-38, 53, 54