Transcript Pre-AP Pre-Calculus Chapter 4, Section 1

Pre-AP Pre-Calculus
Chapter 4, Section 1
Angles and Their Measures
2013 - 2014
Chapter 4
• Welcome to Trigonometry!!
• Pay attention to the difference between degrees
and radians.
• Primarily in this course and Calculus you will use
radians.
Definition: Radian
• A central angle of a circle has measure 1 radian if it
intercepts an arc with the same length as the radius
Degrees and Radians
• A degree is a unit of angular measure equal to
1/180th of a straight angle.
• In DMS (degree-minute-second) system, each
degree is subdivided into 60 minutes (denoted by ‘)
and each minute is subdivided into 60 seconds
(denoted by “).
Working with DMS
Measure
• Convert 42°24’36” to degrees
Working with DMS
Measure
• Convert 37.425° to DMS
Degree - Radian
• A straight angle (line) has __________ and a radian
measure of _________.
Working with Radian
measures
• How many radians are in 90 degrees?
Working with Radian
measures
• How many degrees are there in
𝜋
3
radians?
Working with Radian
measures
• How many degrees are in
2𝜋
3
radians?
Circular Arc Length
Arc Length Formula (Radian
measure)
• If θ is a central angle in a circle of radius r, and if θ is
measured in radians, then the length s of the
intercepted arc is given by
𝑠 = 𝑟𝜃
Arc Length Formula (degree
measure)
• If θ is a central angle in a circle of radius r, and if θ is
measured in degrees, then the length s of the
intercepted arc is given by
𝜋𝑟𝜃
𝑠=
180
Perimeter of a Pizza Slice
• Find the perimeter of a 60° slice of a large (7 inch
radius) pizza.
Designing a Running Track
• The running lanes at the Emery Sears track at
Bluffton College are 1 meter wide. The inside radius
of the lane 1 is 33 meters and inside radius of lane 2
is 34 meters. How much longer is lane 2 than lane 1
around one turn?
Angular and Linear Motion
• Sometimes it is necessary to connect angular speed
(measured in units like revolutions per minute) and
linear speed (measured in units like miles per hour.
• The connection is usually given by one of the arc
length formulas or by a conversion.
Using Angular speed
• Albert’s truck has wheels 36 inches in diameter. If
the wheels are rotating at 630 rpm (revolutions per
mintue), find the truck’s speed in miles per hour.
Ch 4.1 Homework
• Pg. 356 – 357, #’s: 2 – 24 even, 25, 30, 31, 36, 41, 45
59, 61
• 20 total problems
• Gray book: pg. 325