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