1.
2.
3.
4.
Objectives:
To find coterminal,
angles
To convert between
degrees and radians
To find
complementary and
supplementary
To find arc measure
and length
•
•
•
•
•
•
•
Assignment:
P. 290: 17-20 S
P. 291: 21-24 S
P. 291: 39-42 S
P. 291: 47-50 S
P. 291: 51-54 S
P. 291: 55-70 S
P. 292: 79-90 S
You will be
able to find
coterminal
angles
Sketch each of the following angle measurements. To
do so, start by drawing a circle with the x- and y-axes,
and then put your angle into standard position. Do
both on the same circle.
1. 210°
2. −150°
We’ve already figured
out that we can
have angles with
measures greater
than 180°. But we
can just as easily
have angles with
measures greater
than 360°, just ask
Shaun White.
We can totally
have angles
greater than
360°.
We’ve already figured
out that we can
have angles with
measures greater
than 180°. But we
can just as easily
have angles with
measures greater
than 360°, just ask
Shaun White.
What does a 390° angle look like?
It looks just like a 30° angle, except it has made a full
revolution.
Both 30° and 390° have
terminal rays in the
same position, as
such they are called
coterminal angles.
From Exercise 1, 210°
and −150° were also
coterminal angles.
Angles that have the same
initial and terminal sides are
called coterminal angles.
• Coterminal angles can be
found by adding or
subtracting a multiple of 360°
• Any angle has infinitely many
coterminal angles
Draw each of the following angles. Give both a
positive and a negative coterminal angle for
each.
1. 135°
2. −50°
Angles that have the same
initial and terminal sides
are called coterminal
angles.
• Coterminal angles can be
found by adding or
subtracting a multiple of 2π
• Any angle has infinitely
many coterminal angles
Draw each of the following angles. Give both a
positive and a negative coterminal angle for
each.
1. −5π/3
2. 11π/4
You will be
able to convert
between
degrees and
radians
In trigonometry, there’s a
circle with radius one
unit that is
uncommonly useful.
We’ve already laid the
foundation for this unit
circle. Let’s now
transfer all of that
hard-won knowledge
to a nifty worksheet.
Convert the following degree measures to
radian measures.
1.
2.
3.
4.
180°
60°
150°
210°
5.
6.
7.
8.
225°
330°
360°
361°
Convert the following radian measures to
degree measures.
1.
2.
3.
4.
π
π/3
π/6
4π/3
5.
6.
7.
8.
7π/4
11π/6
2π
1
When the angle measure we are converting lies
on our unit circle, it’s elementary to change
units. Sometimes, however, it would be more
convenient to use the conversion factor
below:
π radians = 180°
Now you could set up a proportion or do
something with train tracks.
Convert the following degree measures to
radian measures.
1. 120°
3. −80°
2. −300°
4. 361°
Convert the following radian measures to
degree measures.
1. 3π/4
3. −3π
2. 3π/5
4. 1
You will be able to
find
complementary
and
supplementary
angles
m1  m2  90
m3  m4  90
m5  m6  180
m7  m8  180
m1  m2   / 2
m3  m4   / 2
m5  m6  
m7  m8  
If possible, find the complement and the
supplement of each angle.
1. π/6
2. 5π/6
Find the missing angle measure in radians.
1.
2.
You will be able to
find arc measure
and arc length
The measure of an arc
is the measure of the
central angle it
intercepts. It is
measured in degrees.
An arc length is a
portion of the
circumference of a
circle. It is measured
in linear units and
can be found using
the measure of the
arc.
• Arc measure = mC
– Amount of rotation
• Arc length:
mC
s
 2 r
360
– Actual length
Find the measure and the length of arc AB.
The formula for arc length as learned in
geometry (and 2 slides ago) assumed the
central angle was in degrees. Convert this
formula to radians.
When the central angle
θ of a circle is
measured in radians,
then the length s of
the arc that
intercepts θ is
s  r
Find the measure and the length of arc AB.
Find the measure of θ.
1.
2.
3.
4.
Objectives:
To find coterminal,
angles
To convert between
degrees and radians
To find
complementary and
supplementary
To find arc measure
and length
•
•
•
•
•
•
•
Assignment:
P. 290: 17-20 S
P. 291: 21-24 S
P. 291: 39-42 S
P. 291: 47-50 S
P. 291: 51-54 S
P. 291: 55-70 S
P. 292: 79-90 S