Section+4.1

=//WELCOME TO// //TRIGONOMETRY!!// =  __4.1 Angles and Their Measures__
 * To embrace the new semester, Mr. Maurer opened the second half of the year by finally welcoming us to TRIG. Because the material we will be learning is new for everyone he assured us that this half of the year begins on a level playing field. He was barely able to contain his excitement about the up and coming chapters as he stood in front of the class.

' = minutes " = seconds

There are two units of measurement: 1. DEGREES - a degree is 1/180 of a straight angle and we can break 1 degree in to minutes and seconds. 60 minutes = 1 degree, 60 seconds = 1 minute Ex. Convert 37.425 degrees into DMS (degrees, minutes, seconds) .425 degrees x 60 min/1 degree = 25.5' 5.5" x 60 sec/1 min = 30" Answer: 37 degrees 25' 30"

Ex. (go backwards) Convert 42 degrees 24' 36" into DO (decimal degrees) 36" x 1 min/60 sec = .6' 24.6' x 1 degree / 60 min = .41 degrees Answer: 42.41 degrees

2. RADIANS - a central angle of a circle has measure 1 radian if it intercepts an arc with the same length as the radius. Formula: "theta" is the angle measured in radians theta = s (length of the arc) / r (radius)

Degrees & Radians Circumference = 2 x pi x r = s How many radians are in an entire circle? theta = s/r = 2pir/r = 2pi radians How many degrees? 360/2 = 2pi/2 radians --- 180 degrees = pi radians

Ex. Convert 90 degrees to radians 90 degrees x pi/180 degress = pi/2

Ex. Convert pi/3 radians to degrees pi/3 x 180 degrees/pi = 60 degrees

Ex. Find the length of an arc intercepted by a central angle of 1/2 radians in a circle of radius 5 inches theta = s/r s = theta x r = 1/2 x 5 = 2.5 inches

HW: pg. 356 #1-37 odd **