This preview shows page 1. Sign up to view the full content.
Rev. 2
REVIEW SHEET #1:
Trigonometry and Vector Algebra
Trigonometry:
c
cos
θ
= b/c
a
sin
θ
= a/c
90
°
θ
tan
θ
= a/b
b
a
2
+ b
2
= c
2
because
sin
2
θ + cos
2
θ = 1
How to specify a Vector:
A vector has a magnitude and a direction.
If a rectangular x, y, zcoordinate system is defined, a vector
A
r
is fully specified
in terms of its x, y, and zcomponents; using unit vector notation it is written as
k
A
j
A
i
A
A
z
y
x
ˆ
ˆ
ˆ
+
+
=
r
The magnitude of this vector
A
r
is
2
2
2
x
y
z
A
A
A
A
=
+
+
r
For such 2D vectors the magnitude is
2
2
x
y
A
A
A
=
+
r
and the direction relative to
the positive xaxis is
atan
y
x
A
A
θ
=
.
Conversely, if the vector
A
r
has been specified in terms of its magnitude
A
r
and
its direction θ (measured counterclockwise from the positive xaxis), the x and y
components can be found as follows:
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 09/11/2011 for the course PHYS 0174 taught by Professor Kohler during the Spring '08 term at Pittsburgh.
 Spring '08
 KOHLER
 Physics

Click to edit the document details