Transcript Algebra II Honors

Academy
Algebra II/Trig
Pre-Calculus (4.1)
7.1: Angles and
Their Measure
HW tonight:
p.513 (11-22 all)
HW tomorrow:
p.513 (24-62
even)
Angles
 The
initial side of an angle coincides with the
positive x-axis.
 Positive angles are generated by a
counterclockwise rotation and a negative angle by
a clockwise rotation.
Coterminal Angles
 Angles
with the same initial and terminal sides are
coterminal angles.


Alpha and beta are
coterminal angles.
Radian Measure
 One
radian is the measure of a central angle
that intercepts an arc s equal in length to the
radius r of the circle.
sr
r

r

Radian Measure
the circumference of the circle is 2r , it
follows that a central angle of one full revolution
corresponds to an arc length of 2r . Therefore, 2

radians corresponds to 360 .
 Because
2
Radian Measure
 Other
common angles: 
2
Identify the
Following angles:
0,  ,
3 , and 2 .
2

3 
4
6
Determine the quadrant in which the
angle lies. (The angle is given in radian
measure.)
4
7
1.)
2.)
5
4
3.) -1
5.) 
4.) 5.63

10
7
6.) 
12
Sketch the angle in standard position.
Determine two coterminal angles in
radian measure (one positive & one
negative) for the given angle.
7
1.) 
2
5
2.)
6
Sketch the angle in standard position.
Determine two coterminal angles in
radian measure (one positive & one
negative) for the given angle.
7
3.)
4
2
4.)
3
Determine the quadrant in which the
angle lies.

1.)
7.9
3.)
 260.25

2.)
275.5
4.)
 2.4


Sketch the angle in standard position.
Determine two coterminal angles in
degree measure (one positive & one
negative) for the given angle.
1.)
 120
2.)

270

Find (if possible) the complement
and supplement of the angle.
 Two
positive angles are complementary if their
sum is  2 . Two positive angles are
supplementary if their sum is  .

1.)
12
5
2.)
6
3.) 3
4.) 1.5
Find (if possible) the complement
and supplement of the angle.
1.)
3.)
87
130
2.)

4.)
167 
52

Do Now: Sketch the angle in standard
position. Determine two coterminal
angles in degree measure (one positive
& one negative) for the given angle.

1.)
114
2.)
 445

Convert degrees to radians


180

1 
180
rad
1 rad 

Express the angle in radian
measure as a multiple of pi.
1.) 315



270
3.)
2.) 120

4.) 144

Convert the angle measure from
degrees to radians. Round your
answer to three decimal places.


1.)  46.52
2.) 83.7
Express the angle in degrees.
7

1.)
2.)

12
15
3.)
6
9
28
4.)
15
Convert the angle measure from
radians to degrees. Round your
answer to three decimal places.
8
1.)
2.) 4.8
13
Convert the angle to decimal form.
 60
minutes = 1 degree
 60 seconds = 1 minute
1.)

275 10
'
2.)

9 12
'

'
DMS
3.)
"
 125 36

"

Convert the angle to D M S form.
'
"
 60
minutes = 1 degree
 60 seconds = 1 minute
1.)
310.75

2.)
 345.12

Do Now: Round your answers to three
decimal places. Convert the angle
measure from degrees to radians.


1.) 0.54
2.) 395
Convert the angle measure from
radians to degrees.
3.) 6.5
4.) -0.48

Convert the angle to D M S form.
 60
minutes = 1 degree
 60 seconds = 1 minute
3.)
 0.355
4.)
0.7865
'
"
Arc Length
s  r where  is measured in radians.
4
240 
radians
3

  240 
r4
s  r
 4 
s  4

 3 
16
s
 16.76
3
Find the radian measure of the central
angle of a circle of radius r that
intercepts an arc of length s.
1.) r = 22 feet, s = 10 feet
2.) r = 80 km, s = 160 km
Find the length of the arc on a circle of
radius r intercepted by a central angle
of  .
1.) r = 9 feet,   60 
3
radians
2.) r = 40 cm,  
4