Download Pre-Calculus 4 - Brown Deer Middle/High School

Pre-Calculus 4.1
Triga-whatetry?
Angles in the coordinate plane
The initial side of an angle is __________________________. In
standard position the _________________ is the initial side.
The terminal side of an angle is ________________________.
When the angle is made by rotating in a counterclockwise direction
we have a _________________. When the angle is made by
rotating in a clockwise direction we have a _________________.
Coterminal angles are angles that share ____________________
and _______________________.
What is a radian?
A radian is a unit used to measure angles. How it was derived is
shown on p.361
r
s=r
θ
r
One radian is the measure of a central angle θ that intercepts an arc
s equal in length to the radius r of the circle.
So to find an angle measure in radians: θ =
In one full revolution there are _____ radians. Fill in the graph in
radians.
______
Quadrant ____
Quadrant ____
______
______
Quadrant ____
Quadrant ____
______
Note: When a number is written without units, radians are
assumed. In order to mean degrees you must put the degree
symbol. If you don’t see the degree symbol, then it is radians.
Degrees/Minutes/Seconds
I think you already know a lot about degrees so…in one full
revolution there are _____ degrees.
But what does 24˚ 35’ 16” mean?
Write in decimal form to the nearest thousandth.
1) 147˚ 50’ 20”
2) -36˚ 42’ 19”
Write in degrees-minutes-seconds form to the nearest second.
3) 46.345˚
4) 248.877˚
Converting from radians to degrees
180˚ = _______ radians
1) Convert from radians to degrees.
a)
2
3
b)
5
8
c)
23
18
d) 5
Converting from radians to degrees
2) Convert from degrees to radians.
a) 235˚ 15’
b) -48˚ 20’ 52”
c) 56˚
d) 540˚
Finding coterminal angles
What are coterminal angles?
3) Find two angles that are coterminal to:
a) 172˚ 12”
b) -420˚
c) 
3
4
d)
13
6
Complementary and Supplementary angles in radians
In degrees complementary angles add up to ________.
In radians complementary angles add up to ________.
In degrees supplementary angles add up to ________.
In radians supplementary angles add up to ________.
Arc Length
In geometry you learned, in order to find an arc length s in a circle:
centralangle
s  2r
360
Now that we know radians:
s  r
where θ is measured in radians
4) A circle has a radius of 6 inches. Find the arc length
intercepted by an angle of 200˚.
5) A circle has a radius of 12 cm. Find the arc length intercepted

by an angle of .
6
6) A circle has a radius of 15 feet. Find the arc length intercepted
by an angle of 4 radians.
7) Use unit analysis to find the linear speed of a bicycle when the
20 inch diameter wheels are spinning at 250 rpms.
Assignment:p.367#5-9odds,15-27odds,39-61odds,71-81odds,96