# 4.1_Angles_and_Their_Measure

Document Sample

```					       Chapter 4
Trigonometric Functions
Background

•The term trigonometry is derived from ancient
Greek roots meaning “three side measure”.
•It is the study of ratios within right triangles.
•Trigonometry came about in the ancient world
when the transition was made from a flat earth
to a world of circles and spheres.
•Today it is used to understand everything from
electrical current to modern
telecommunications.
•Any type of periodic (recurring) behavior can
be modeled using trigonometric functions.
Section 4.1
Angles and Their
Measure
Warm-up
Warm-up
Angle

Vertex
90°
Standard
y

Position

180°                          0°
O Initial side
x

270°
Degree

•A degree, represented by the symbol °,
is a unit of angular measure equal to
1/180th of a straight angle.
•In the DMS(degree-minute-second)
system of angular measure, each degree is
subdivided into 60 minutes (denoted ´)
and each minute is subdivided into 60
seconds (denoted´´)
Example 1: Working with DMS Measure

1. Convert 37.425° to DMS.

2. Convert 42°24´36´´ to degrees.

A radian is the measure of a central angle
θ that intercepts an arc “s” equal in
length to the radius “r” of the circle.
s
θ ,
y

r       s=r              r
where θ is
θ
r               measured in
x
Radians are the angle measures used in
calculus.
2π             360
360             2π
π                         180
180                         π
Formula to go from    Formula to go from
π
y

2

3π
2
Example 2: Working with
1. How many radians are in 60 degrees?

2. How many radians are in 150 degrees?
Example 2: Working with
3. How many degrees are in π/4 radians?

4. How many degrees are in 3π/5 radians?
Arc Length

For a circle of radius “r”, a central angle θ
intercepts an arc of length “s” given by
s = rθ
where θ is measured in radians.
Example 3: Finding arc length

1. A circle has a radius of 27 inches.
Find the length of the arc
intercepted by a central angle of
160°. Give the answer in terms of π
and rounded to the nearest
hundredth.
π    8π
180    9

2.   Find the arc length.

8π
s     27  24π inches  75.40inches
9
Example 3: Finding arc length

2. Find the perimeter of a 30° slice of a
Example 3: Finding arc length

3. A 100-degree arc of a circle has a
length of 7 cm. To the nearest
centimeter, what is the radius of the
circle?
Example 3: Finding arc length

4. The concentric circles on an archery
target are 6 inches apart. The inner
circle (red) has perimeter of 37.7 inches.
What is the perimeter of the next
largest (yellow) circle?
Example 4

John’s truck has wheels 36 inches in
diameter. If the wheels are rotating at
630 rpm (revolutions per minute), find the
truck’s speed in miles per hour.

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 6 posted: 9/1/2012 language: English pages: 24