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 initial vertex 270 º

1.) 50º2.) 130º 3.) 260 º 4.) 310º

1.) -50º2.) -180º 3.) -240 º 4.) -300º

 Angles that share the same terminal side  Differ by 360º (or a multiple of 360 ie. 720)  Example 4 vs example 1  To find positive and negative coterminal angles- add and subtract 360 º  1.) 210º2.)-180º3.) 400º

 Radians are a 2 nd way to measure an angle  Positive and negative radian measures:

1.)2.) 3.) 4.)

1.)2.) 3.) 4.)

 Differ by  To find a positive and negative coterminal angle, add and subtract 1.) 2.) 3.)

 Degree to radian: Multiply by 1.)2.) 3.)  Radian to degree: Multiply by 1.) 2.) 3.)

 Complementary angles- angles whose sum = 90  Supplementary angles- angles whose sum = ) 45 º 2.) 61 º 3.) 100 º

 A degree, represented by the symbol °, is a unit of angular measure equal to 1/180 th 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 “).

 Convert ° to DMS.  Convert 42°24’36” to degree.

 Arc length- measures a segment (arc) of a circle  must be in radians  1.) 2.)

 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.

 Angular speed is measured in units like revolutions per minute.  Linear speed is measured in units like miles per hour.

 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 odd, even, odd, all, 96, 99