1.4 Trigonometry

1
1.4 Trigonometry
2
Sine, Cosine, and Tangent
3
Sine, Cosine, and Tangent
4
Sine, Cosine, and Tangent
5
Pythagorean Theorem
6
What if the triangle is not a right-triangle?
7
Law of Cosines andLaw of Sines
Law of cosines is given by,
Law of sines is given by,
8
1.5 Scalars and Vectors
9
1.5 Scalars and Vectors
Many physical quantities are used in physics,
which are divided into scalars and vectors.
10
1.5 Scalars and Vectors
Many physical quantities are used in physics,
which are divided into scalars and vectors. A
scalar quantity is one that can be described by a
single number (including any units) giving its
size or magnitude. Examples Time, volume, mass,
temperature, and density.
11
1.5 Scalars and Vectors
Many physical quantities are used in physics,
which are divided into scalars and vectors. A
scalar quantity is one that can be described by a
single number (including any units) giving its
size or magnitude. Examples Time, volume, mass,
temperature, and density. A quantity that deals
inherently with both magnitude and direction is
called a vector quantity. Examples Force,
weight, velocity, and displacement.
12
Vector Illustration
Consider the following displacement vector of a
car
13
Vector Illustration
Consider the following displacement vector of a
car
The length of the vector arrow is proportional to
the magnitude of the vector and the arrow
represents the direction.
14
Vector Illustration
Consider the following displacement vector of a
car
The length of the vector arrow is proportional to
the magnitude of the vector and the arrow
represents the direction. In the text, bold face
is used for vectors and italics is used for
scalars. When hand written an arrow is placed
above the symbol.
15
1.6 VECTOR ADDITION
Addition of two co-linear displacement vectors A
and B, both are due East. (A 275-m, B 125-m)
16
1.6 VECTOR ADDITION
What if vector B (125-m) is due West?
17
1.6 VECTOR ADDITION
What if vector B is 275-m, due West?
18
1.6 VECTOR ADDITION
Addition of two perpendicular displacement
vectors A and B.
19
1.6 VECTOR ADDITION
Addition of two displacement vectors A and B,
neither colinear nor perpendicular, using
graphical method.
20
1.6 VECTOR ADDITION
Addition of two displacement vectors A and B,
neither colinear nor perpendicular, using laws of
sines and cosines.
21
SUBTRACTION