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1.4 Trigonometry. Sine, Cosine, and Tangent. Sine, Cosine, and Tangent. Sine, Cosine, and Tangent. Pythagorean Theorem. What if the triangle is not a right-triangle?. Law of Cosines and Law of Sines. Law of cosines is given by, . Law of sines is given by,. 1.5  Scalars and Vectors.

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Presentation Transcript
law of cosines and law of sines
Law of Cosines andLaw of Sines

Law of cosines is given by,

Law of sines is given by,

1 5 scalars and vectors9
1.5 Scalars and Vectors

Many physical quantities are used in physics, which are divided into scalars and vectors.

1 5 scalars and vectors10
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.

1 5 scalars and vectors11
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.

vector illustration
Vector Illustration

Consider the following displacement vector of a car:

vector illustration13
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.

vector illustration14
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.

1 6 vector addition
1.6 VECTOR ADDITION

Addition of two co-linear displacement vectors A and B, both are due East. (A = 275-m, B = 125-m)

1 6 vector addition16
1.6 VECTOR ADDITION

What if vector B (125-m) is due West?

1 6 vector addition17
1.6 VECTOR ADDITION

What if vector B is 275-m, due West?

1 6 vector addition18
1.6 VECTOR ADDITION

Addition of two perpendicular displacement vectors A and B.

1 6 vector addition19
1.6 VECTOR ADDITION

Addition of two displacement vectors A and B, neither colinear nor perpendicular, using graphical method.

1 6 vector addition20
1.6 VECTOR ADDITION

Addition of two displacement vectors A and B, neither colinear nor perpendicular, using laws of sines and cosines.