MATH
1316
–
Trigonometry
–
Review
for
Exam
2
Show
your
work
and
do
not
write
on
this
sheet.
Make
sure
you
practice
filling
out
the
unit
circle.
And
know
these
formulas:
Arc
length:
s = rθ 1
Area
of
a
sector:
A = r 2θ 2
€ v = s or
v = rω Linear
speed:
t
θ
€
Angular
speed:
ω = t
€
€
Convert
the
degree
measure
to
radians:
1)
45°
2)
175°
3)
800°
€
Convert
the
radian
measure
to
degrees:
5π
8π
21π
4)
5)
6)
−
4
3
5
€
7)
The
radius
of
a
circle
is
15.2
cm.
Find
the
length
of
an
arc
of
the
circle
intercepted
by
a
central
3π
€
€
angle
of
radians.
4
8)
Find
the
length
of
an
arc
intercepted
by
a
central
angle
of
0.769
radian
on
a
circle
with
radius
11.4
cm.
€
9)
Find
the
measure
(in
degrees)
of
a
central
angle
that
intercepts
an
arc
of
length
7.683
cm
in
a
circle
of
radius
8.973
cm.
7π
radians
forms
a
sector
of
a
circle.
Find
the
area
of
the
sector
if
the
4
radius
of
the
circle
is
28.69
in.
10)
A
central
angle
of
11)
Find
the
area
of
a
sector
of
a
circle
having
a
central
angle
of
21° 40′ in
a
circle
of
radius
38.0m.
€
12)
Find
the
measure
of
the
central
angle
θ
(in
radians)
and
the
area
of
the
sector.
€
Find
each
exact
function
value.
Do
not
use
a
calculator.
 5π 
 11π 
π
2π
5π
13)
tan 14)
cos 15)
sin−  16)
csc−
 17)
cot
 6 
 6 
3
3
4
€
Use
a
calculator
to
find
an
approximation
(4
decimal
places).
Set
your
calculator
in
radian
mode.
18)
cot
3.0543
19)
sec
7.3159
€
€
€
€
 π
Find
the
value
of
s
in
the
interval
0,  that
makes
the
statement
true.
 2
20)
tan
s
=
4.0112
21)
csc
s
=
1.2361
Find
the
exact
value
of
s
in
the
given
interval
that
has
the
given
value.
Do
not
use
a
calculator.
€
 π
π 
2
22)
0, ; cos s =
23)
 , π ; tan s = − 3  2
2 
2
€
24)
Find
the
linear
speed
of
a
point
on
the
edge
of
a
flywheel
of
radius
7
cm
if
the
flywheel
is
rotating
90
times
per
second.
€
25)
A
Ferris
wheel
has
a
radius
25
ft.
If
it
takes
30
seconds
for
the
wheel
to
turn
5 6
radians,
what
is
the
angular
speed
of
the
wheel?
26)
It
takes
Jupiter
11.86
years
to
complete
one
orbit
around
the
sun.
Jupiter’s
average
distance
from
the
sun
is
438,800,000
miles.
Find
its
orbital
speed
(linear
speed
along
its
orbital
path)
in
miles
per
second.
€
€
€
€
€
€
€
€
€
€
€
Graph
each
function
over
a
one
period
interval.
27)
y = 3sin x 1
28)
y = sec x 2
29)
y = −tan x 30)
y = 2 + cot x 31)
y = tan 3x 32)
y = 3cos2x 1
33)
y = cot 3x 2

π
34)
y = cos x −  
4

π
35)
y = sin 3x +  
2
36)
y = 1+ 2cos 3x 37)
y = −1− 3sin2x €
€
€
€
38)
y = 2sin πx 1
39)
y = − cos(πx − π ) 2
40)
y = −csc2x 41)
y = −1+ 2sin(x + π ) Determine
the
simplest
form
of
an
equation
for
each
graph.
Chose
b
>0
and
include
no
phase
shifts.
42)
43)