Name
Unit 1: Correlates to text 3-1 & 3-2
Vector Operations and Trigonometry
Your Notes go here:
Quantities that are described with just a number, that is, quantities that have magnitude
only are
.
That is, scalars have
Examples:
but no
.
-
More descriptive quantities that have both magnitude and direction are
Examples:
.
-
Vectors are represented as
.(
)
of a vector is represented by its length.
of a vector is
represented by its direction
Example: Using scale drawing
In order to combine vectors, they must represent
.
When combining vectors, the order you combine them in is
.
That is, you can
answer.
and still get the same
You can move them around, but you can’t change their
.
or
The sum of any number of vectors is called the
.
Demo notes:
To combine vectors, use the




method.
Draw the vectors lining them up so that the
of the first vector
touches the
of the second vector. (Remember, order doesn’t matter!)
Draw
from the start of the
vector to
the end of the
vector. This is called the resultant.
Use a ruler to measure the
of the resultant, and use your
to determine the
of your
resultant.
Use a
to measure the direction of the resultant.
Example: Adding vectors
Example: Subtracting vectors
To solve vector problems analytically, we use basic
.
Trig for Physics
When defined on a right triangle such as the one shown here, sin, cos and tan are
defined as the ratio of
.
The side opposite the right angle is called the
(
The side directly opposite the angle  is called the
side because…well, it’s obvious  .
).
(
The side that, along with the hypotenuse, makes the angle  is called the
(
) side.
The sin, cos and tan are defined as follows:
sin𝜃 =
cos𝜃 =

tan𝜃 =
Exercises: Consider the triangle drawn and identify the value of each trig function
indicated.
B
sin A=
sin B=
cos A=
cos B=
tan A=
tan B=
5
4
A
3
When you are given two sides of a right triangle, use the
to find the third side.
)
When you are looking for the angle, use two sides of the right triangle and the
.
Example: A 65 meter rope is connected to the top of a building, and is attached to the
ground 50 meters from the building. What angle does the rope make with the ground? And
how tall is the building?
Example: A projectile has an initial horizontal velocity of 5 m/s and an initial vertical
velocity of 3 m/s upward. At what angle was the projectile fired?
Breaking a vector into its vertical and horizontal parts is called
and the pieces are called its
.
Question:
The equilibrant of a resultant is exactly
in direction.
The equilibrant
vectors.
in magnitude and
the effect of all the combined