Final Exam Review Guide
Math 1220
Spring 2012
A Note on the Exercises: There are A LOT of suggested exercises here. The exercises are subdivided in the book. It
is unreasonable to have any sort of expectation of doing all of them; but try to do some exercises from each subdivision
and from the nonbook ones.
•
Chapter 12 Trigonometry
–
12.1 Measurement of Angles
*
Terms: angle, initial ray, terminal ray, vertex, standard position, degree, radian, unit circle, coterminal
angles
*
Converting Degrees to Radians:
f
(
x
) =
π
180
x
radians
where
x
is the number of degrees and
f
(
x
) is the number of radians.
*
Converting Radians to Degrees:
g
(
x
) =
180
π
x
degrees
where
x
is the number of radians and
g
(
x
) is the number of degrees.
*
Know how to identify when two angles are coterminal.
*
Exercises: pp.763 126
–
12.2 The Trigonometric Functions
*
Terms: sine, cosine, periodic, trigonometric identities
*
cos(
θ
) is the
x
coordinate of the point on the unit circle
θ
radians away from the positive
x
axis (p.765).
*
sin(
θ
) is the
y
coordinate of the point on the unit circle
θ
radians away from the positive
x
axis (p.765).
*
tan =
sin
cos
*
Can also think of sin
,
cos
,
tan in terms of right triangles: (SOH)(CAH)(TOA).
*
sec
x
=
1
cos
x
,
csc
x
=
1
sin
x
,
cot
x
=
1
tan
x
*
Know
the
values
of
these
six
functions
at
the
common
angles:
0
,
π
6
,
π
4
,
π
3
,
π
2
,
2
π
3
,
3
π
4
,
5
π
6
, π,
7
π
6
,
5
π
4
,
4
π
3
,
3
π
2
,
5
π
3
,
7
π
4
,
11
π
6
(from the formulas above, you only need to know these for sin and cos.)
See table 2 on p. 766.
*
Identities:
·
sin(

θ
) =

sin
θ
·
cos(

θ
) = cos
θ
·
sin
2
θ
+ cos
2
θ
= 1
·
tan
2
θ
+ 1 = sec
2
θ
·
cot
2
θ
+ 1 = csc
2
θ
·
cos
2
θ
=
1
2
(1 + cos 2
θ
)
·
sin
2
θ
=
1
2
(1

cos 2
θ
)
·
sin(
A
±
B
) = sin
A
cos
B
±
cos
A
sin
B
·
cos(
A
±
B
) = cos
A
cos
B
∓
sin
A
sin
B
·
sin 2
A
= 2 sin
A
cos
A
·
cos 2
A
= cos
2
A

sin
2
A
1