Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side...
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Transcript of Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side...
Section 4.1
Trigonometry: the measurement of angles Standard Position: Angles whose initial
side is on the positive x-axis 90º
terminal 180º 0º
initialvertex
270º
1.) 50º 2.) 130º
3.) 260º 4.) 310º
1.) -50º 2.) -180º
3.) -240º 4.) -300º
Angles that share the same terminal side
Differ by 360º (or a multiple of 360 ie. 720)
Example 4 vs example 1To find positive and negative
coterminal angles- add and subtract 360º
1.) 210º 2.)-180º 3.) 400º
Radians are a 2nd way to measure an angle
Positive and negative radian measures:
1.) 2.)
3.) 4.)
5
6
6
5
4
11
6
1.) 2.)
3.) 4.)
5
6
3
7
9
5
13
4
Differ by To find a positive and negative
coterminal angle, add and subtract
1.) 2.) 3.)
2
2
3 3
4
5
6
Degree to radian: Multiply by 1.) 2.) 3.)
Radian to degree: Multiply by 1.) 2.) 3.)
180
180
Complementary angles- angles whose sum = 90
Supplementary angles- angles whose sum = 180
1.) 45º 2.) 61º 3.) 100º
DMS
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 by ‘) and each minute is subdivided into 60 seconds (denoted by “).
Working with DMS measure
Convert 37.425° to DMS.
Convert 42°24’36” to degree.
Arc length- measures a segment (arc) of a circle
must be in radians
1.) 2.)
S r S
35,
4r
43,
5r
Arc Length
Degree Measure
Find the length of an arc that subtends a central angle with measure 120 degrees in a circle with a radius of 5 inches.
180
rs
Angular and Linear Speed
Angular speed is measured in units like revolutions per minute.
Linear speed is measured in units like miles per hour.
Linear Speed
Angular Speed
Jaxen’s truck has wheels 36 inches in diameter. If the wheels are rotating at 630 rpm (revolutions per minute), find the trucks speed in miles per hour.
Homework
Page 265-26811-19 odd, 40-46 even, 59-69 odd, 81-
84 all, 96, 99