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Some Equations for Exam 1
•
sin 30
◦
=
1
2
=0
.
50;
cos 30
◦
=
√
3
/
2
±
0
.
87
•
sin 60
◦
=
√
3
/
2
±
0
.
87;
cos 60
◦
=
1
2
.
50
•
sin 45
◦
=
√
2
/
2
±
0
.
71;
cos 45
◦
=
√
2
/
2
±
0
.
71
•
For vectors
±
A
=
A
x
ˆ
i+
A
y
ˆ
j+
A
z
ˆ
k and
±
B
=
B
x
ˆ
B
y
ˆ
B
z
ˆ
k:

±
A

=
A
=
±
A
2
x
+
A
2
y
+
A
2
z
;
±
A
·
±
B
=
AB
cos
θ
=
A
x
B
x
+
A
y
B
y
+
A
z
B
z
;
±
A
×
±
B
=(
A
y
B
z

A
z
B
y
)
ˆ
i+(
A
z
B
x

A
x
B
z
)
ˆ
j+(
A
x
B
y

A
y
B
x
)
ˆ
k;

±
A
×
±
B

=
AB
sin
θ
.
•
For a function of the form
f
(
x
)=
ax
n
, where
n
is an integer,
df
dx
=
nax
n

1
and
²
f
(
x
)
dx
=
a
n
+1
x
n
+1
+
C
.
•
If a particle’s position is represented by
±r
=
(
t
),
±v
=
d±r
dt
and
±a
=
d±v
dt
=
d
2
dt
2
.
Therefore,
v
x
(
t
³
a
x
(
t
)
dt
+
C
and
x
(
t
³
v
x
(
t
)
dt
+
C
, and similarly for
y

and
z
components.
•
For a constant acceleration
,
(
t
0
+
0
t
+
1
2
±a t
2
and
(
t
0
+
where
0
and
0
are the position and velocity at time
t
= 0, respectively.
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This note was uploaded on 07/30/2008 for the course PHY 317k taught by Professor Kopp during the Spring '07 term at University of Texas at Austin.
 Spring '07
 KOPP

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