Medias Angulares:
ÁNGULO
1. Ángulo en posición normal.
2. Ángulo de referencia.
SISTEMA ANGULAR
1. Sistema sexagesimal o en grados.
2. Ángulos coterminales o Sentidos angulares.
3. Ángulos especiales.
Obj. 8 Classifying Angles and Pairs of Anglessmiller5
The student will be able to (I can):
Correctly name an angle
Classify angles as acute, right, or obtuse
Identify
linear pairs
vertical angles
complementary angles
supplementary angles
and set up and solve equations.
Angles: Classifications; Measuring; and DrawingJames Smith
Discusses the concept of measurement in general before exploring how we might define a unit of measure for angles, and design a tool for the purpose (which, in its refined version, is what we now call a "protractor"). Shows how to use a protractor to draw angles of various sizes, then ends by introducing the concept of the radian measurement.
In this document, I will explain how one can quickly and easily trisect an angle with reasonably high accuracy using only a ruler and a compass.
As one will see that the used methods will result in a trisection with unnoticeable error by the naked eye.
I am well aware of Pierre Laurent Wantzel’s proof from 1837 that trisecting an angle is mathematically impossible.
The inscrutable imaginary number, so useful and yet so intriguing. Explain why this is so and how important it is to quantum mechanics, resulting in the ultimate quantum.
Obj. 8 Classifying Angles and Pairs of Anglessmiller5
The student will be able to (I can):
Correctly name an angle
Classify angles as acute, right, or obtuse
Identify
linear pairs
vertical angles
complementary angles
supplementary angles
and set up and solve equations.
Angles: Classifications; Measuring; and DrawingJames Smith
Discusses the concept of measurement in general before exploring how we might define a unit of measure for angles, and design a tool for the purpose (which, in its refined version, is what we now call a "protractor"). Shows how to use a protractor to draw angles of various sizes, then ends by introducing the concept of the radian measurement.
In this document, I will explain how one can quickly and easily trisect an angle with reasonably high accuracy using only a ruler and a compass.
As one will see that the used methods will result in a trisection with unnoticeable error by the naked eye.
I am well aware of Pierre Laurent Wantzel’s proof from 1837 that trisecting an angle is mathematically impossible.
The inscrutable imaginary number, so useful and yet so intriguing. Explain why this is so and how important it is to quantum mechanics, resulting in the ultimate quantum.
In geometry, there are various types of angles, based on measurement. The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
There are various types of angles in geometry. Angles form the core part of the geometry in mathematics. They are the fundamentals that eventually lead to the formation of the more complex geometrical figures and shapes.
What are Angles
When two rays combine with a common endpoint and the angle is formed. The two components of an angle are “sides” and “vertex”.
Parts of Angle
Vertex – Point where the arms meet.
Arms – Two straight line segments form a vertex.
Angle – If a ray is rotated about its endpoint, the measure of its rotation is called angle between its initial and final position.
Classification of Angles
Angles can be classified into two main types:
Based on Magnitude
Based on Rotation
Six Types of Angles
In Maths, there are mainly 5 types of angles based on their direction. These five angle types are the most common ones used in geometry. These are:
Acute Angles
Obtuse Angles
Right Angles
Straight Angles
Reflex Angles
Full Rotation
Los productos notables que vamos a trabajar en esta guía son:
1. Cuadrado de un binomio.
2. Cuadrado de un trinomio.
3. Producto de la suma por la diferencia.
Límites de funciones indeterminadas:
1. Límite de funciones racionales.
2. Límite de funciones trigonométricas.
3. Límites infinitos.
4. Límites en el infinito.
5. Límites en el infinito de una función racional.
Técnicas de Conteo:
1. Permutaciones sin repeticiones:
1. 1. Tomando todos los elementos.
1. 2. Sin tomar todos los elementos.
2. Combinaciones sin repeticiones.
Cónicas:
Circunferencia.
Ecuación canónica de la circunferencia.
Posiciones relativas de una recta y de una circunferencia en el plano.
Posición relativa de dos circunferencias en el plano.
Números Complejos:
1. Representación gráfica de los números complejos.
2. Conjugado y opuesto de un número complejo.
3. Operaciones con números complejos.
Trabajaremos operaciones multiplicativas:
1. Multiplicación entre polinomios.
2. Multiplicación de un monomio por un polinomio.
3. Multiplicación de un polinomio por otro polinomio.
Polinomios.
Características:
1. GRADO ABSOLUTO DE UN POLINOMIO.
2. TÉRMINOS SEMEJANTES DE UN POLINOMIO.
3. GRADO RELATIVO DE UN POLINOMIO CON RESPECTO A UNA VARIABLE.
4. TÉRMINO INDEPENDIENTE DE UN POLINOMIO.
Tipos de polinomios:
1. POLINOMIO ORDENADO .
2. POLINOMIO COMPLETO.
3. POLINOMIO OPUESTO.
4. VALOR NUMÉRICO DE UN POLINOMIO.
Potenciación y sus propiedades:
1. Producto de Potencia de igual base.
2. Cociente de Potencias de igual base.
3. Potencia de una potencia.
4. Potencia de un producto.
5. Potencias de un cociente.
6. Exponente cero.
7. Exponente enteros negativos.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Home assignment II on Spectroscopy 2024 Answers.pdf
Medidas Angulares
1.
2. ÁNGULO
Grado de apertura (giro o rotación) existente entre dos rectas
que se cortan en un punto común llamado VÉRTICE, la recta que
permanece fija se le llama LADO INICIAL y la recta que gira se
le llamada LADO FINAL.
El ángulo ∡𝐷𝐴𝐸 también se pueden nombrar con la letra
mayúscula de su vértice ∡𝐴 o con las letras minúsculas del
alfabeto griego, por ejemplo α
Lado Inicial
D
A
E
Vértice
𝜶
3. - Si estas dos rectas las hacemos rotarse entre
sí hasta dar una vuelta completa se habrá
formado una circunferencia. El vértice sería el
centro de la circunferencia.
- Si dividimos una circunferencia en cierta
cantidad de partes iguales, formadas por sus
radios, a cada división se le llamará
SEGMENTO CIRCULAR. El grado de
apertura de dicho segmento se llamará una
cantidad o grado angular.
4. Un ángulo está en posición normal cuando su lado inicial se
encuentre sobre el eje positivo 𝑥. Cuando los ángulos están
posicionados en la misma dirección de las agujas del reloj, estos
son NEGATIVOS y cuando están en la dirección contraria a las
manecillas del reloj; son POSITIVOS.
1. ÁNGULO EN POSICIÓN NORMAL
7. Para todo ángulo 𝜃 en posición normal el ángulo de referencia de
𝜃, denotado 𝜃𝑅, es el ángulo positivo menor de 90° formado por
el lado final de 𝜃 y el eje horizontal 𝑥.
2. ÁNGULO DE REFERENCIA
CUADRANTE ÁNGULO LADO
ÁNGULO DE
REFERENCIA
I 0° < 𝜃 < 90° 𝜃𝑅 = 𝜃
II 90° < 𝜃 < 180° 𝜃𝑅 = 180° − 𝜃
III 180° < 𝜃 < 270° 𝜃𝑅 = 𝜃 − 180°
IV 270° < 𝜃 < 360° 𝜃𝑅 = 360° − 𝜃
8. Un ángulo de giro completo o perigonal es aquel que se genera
por una rotación completa del lado final. La medida de este
ángulo es de 360 y se escribe 360°, donde el símbolo ° se lee
grados.
Con respecto a un ángulo de giro completo es importante tener
en cuenta que:
SISTEMA ANGULAR
1. Sistema sexagesimal o en grados
Si un giro completo se divide en 360 partes iguales, entonces,
cada parte es un grado sexagesimal; es decir,
1
360
parte de la
rotación completa es igual a 1°.
9. Si un grado se divide en 60 partes iguales, entonces, cada
parte es un minuto; es decir,
1
60
de grado es igual a 1′
, donde
el símbolo ′ se lee minutos.
Si un minuto se divide en 60 partes iguales, entonces, cada
parte es un segundo; es decir,
1
60
de grado es igual a 1′′,
donde el símbolo ′′ se lee segundos.
Por lo tanto, se concluye que 1° = 60′ = 3600′′
16. Todo ángulo que se cuente en sentido contrario a las manecillas
del reloj (sentido anti-horario) es un ángulo positivo. Todo
ángulo que se cuente en el sentido de las manecillas del reloj
(sentido horario) es un ángulo negativo.
2. Ángulos coterminales o Sentidos angulares
Dos ángulos son coterminales sin tener los mismos lados
iniciales y finales, sin importar su magnitud o sentido.
22. Cuando un ángulo en abertura a una vuelta completa en la
circunferencia este coincide con otro ángulo menor a 360. Para
simplificarlo, simplemente se divide su valor sobre 360 . El
cociente indica el número de vueltas de la circunferencia, y el
residuo indicará el ángulo de coincidencia.
4. Simplificación de ángulos mayores a una vuelta
Por ejemplo, simplificar los ángulos:
4321° 728°
23. Si el ángulo a simplificar es negativo, su resultado será de este
signo, pero a la vez coincidirá con otro ángulo en posición
normal. En la práctica para trabajar con los valores angulares, se
recomienda simplificar completamente el valor dado.
NOTA
Por ejemplo, simplificar los ángulos:
−1310° −750°
