Bell Work
• How many degrees are in a circle?
• How many degrees are in a straight angle?
• Find the measure of
the angle in blue and red.
Introduction to Trigonometry
• History of Trigonometry
https://www.youtube.com/watch?v=PhS_7M8j
Qbo
4.1 Angles and Their Measure
• A degree is a unit of angular measure that you
are familiar with.
• 180 in a straight angle and 360 in a circle
Radians
• A radian is another unit of angular measure.
• A central angle has measure 1 radian if it
intercepts an arc with the same length as the
radius. It intercepts an arc of length 1 radius.
Converting between Degrees & Radians
• The circumference of a circle is _______.
• So a semicircle would have arc length _____.
• A straight angle measures ______ radians.
• A circle measures ______ radians.
Example
We use the conversion factor 180 =  radians
(a) How many radians are in 90?
(b) How many degrees are in /3 radians?
Example – You Try
(a) How many radians are in 240?
(b) How many degrees are in 3/4 radians?
Arc Length
If  is a central angle in a circle of radius r, and if
 is measured in radians, then the length s of
the intercepted arc is given by
s = r
Arc Length in Degrees
s=
𝑟 
180
Example
Find the perimeter of a 60 slice of a large (7 in.
radius) pizza.
Example – You Try
Find the perimeter of a 30 slice of a large (8 in.
radius) pizza.
Example
The running lanes of a certain track are 1 meter
wide. The inside radius of lane 1 is 33 meters
and the inside radius of lane 2 is 34 meters. How
much longer is lane 2 than lane 1 around one
turn?
Homework
4.1 (pg. 325-327)
#10,12,14,18,20,22,26,28,30,38,40,60