Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side...
-
Upload
brian-boone -
Category
Documents
-
view
222 -
download
0
Transcript of Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side...
![Page 1: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/1.jpg)
Section 4.1
![Page 2: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/2.jpg)
Trigonometry: the measurement of angles Standard Position: Angles whose initial
side is on the positive x-axis 90º
terminal 180º 0º
initialvertex
270º
![Page 3: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/3.jpg)
1.) 50º 2.) 130º
3.) 260º 4.) 310º
![Page 4: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/4.jpg)
1.) -50º 2.) -180º
3.) -240º 4.) -300º
![Page 5: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/5.jpg)
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
![Page 6: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/6.jpg)
Radians are a 2nd way to measure an angle
Positive and negative radian measures:
![Page 7: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/7.jpg)
1.) 2.)
3.) 4.)
5
6
6
5
4
11
6
![Page 8: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/8.jpg)
1.) 2.)
3.) 4.)
5
6
3
7
9
5
13
4
![Page 9: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/9.jpg)
Differ by To find a positive and negative
coterminal angle, add and subtract
1.) 2.) 3.)
2
2
3 3
4
5
6
![Page 10: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/10.jpg)
Degree to radian: Multiply by 1.) 2.) 3.)
Radian to degree: Multiply by 1.) 2.) 3.)
180
180
![Page 11: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/11.jpg)
Complementary angles- angles whose sum = 90
Supplementary angles- angles whose sum = 180
1.) 45º 2.) 61º 3.) 100º
![Page 12: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/12.jpg)
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 “).
![Page 13: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/13.jpg)
Working with DMS measure
Convert 37.425° to DMS.
Convert 42°24’36” to degree.
![Page 14: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/14.jpg)
Arc length- measures a segment (arc) of a circle
must be in radians
1.) 2.)
S r S
35,
4r
43,
5r
![Page 15: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/15.jpg)
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
![Page 16: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/16.jpg)
Angular and Linear Speed
Angular speed is measured in units like revolutions per minute.
Linear speed is measured in units like miles per hour.
![Page 17: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/17.jpg)
Linear Speed
![Page 18: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/18.jpg)
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.
![Page 19: Section 4.1. Trigonometry: the measurement of angles Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649d9d5503460f94a86ba3/html5/thumbnails/19.jpg)
Homework
Page 265-26811-19 odd, 40-46 even, 59-69 odd, 81-
84 all, 96, 99