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Use exact values to show that each of the following is

Trigonometry | ISBN: 9780495108351 | Authors: Charles P McKeague ISBN: 9780495108351 200

Solution for problem 5.1.193 Chapter 5.3


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Trigonometry | ISBN: 9780495108351 | Authors: Charles P McKeague


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Problem 5.1.193

Use exact values to show that each of the following is true. sin 60 = 2 sin 30 cos 30

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Week One and Two 01-11-16 to 01-22-16 Anthropology Anthropology is the study of humans. This includes culture, nature and behavior. There are four disciplines of anthropology: 1. Archaeology: The study of past cultures 2. Linguistic: The study of human language and how it is used 3. Culture: Is current and ‘uniquely human’ 4. Biology: The physical and biological study of humans *Note: Culture and Biology seem to contradict each other in humans. - We do not rely on our biology to keep us alive. We can adapt to culture and use culture. We are Biocultural. • We are Homo Sapiens, however, there are other extinct beings that are in the Homo genus. • Scientific theories are more specific, unlike social theories. - Theories cannot be 100% proven in the same way as laws can. Example: The law of gravity verse the theory of evolution. A. When you take a hypothesis and cannot prove it or falsify it - keep in mind that you have to test it over and over again - it becomes a theory. Origins of Human Bipedalism: • Until the year 2000 a theory referred to as Open Savanna was widely accepted. This theory states that early humans/pre-humans started walking in savannas and grew hair on their heads to protect from open sun. However, in 2001 evidence was found bipedal pre-humans in the woodlands. • 1 o 9 Week One and Two 01-11-16 to 01-22-16 What makes a human a human - What are the things that make us different • Class List: 1. Our language 2. Bone Structure (Ex: Bipedalism) 3. Culture (very broad) 4. Our intellect 5. Ability to use tools 6. Emotional - The expression of these emotions* 7. Adapt environment to use - Which of these can be found in history • All of these can, in some way or another, be seen in archeology. *Note: The emotional is the most far reached in terms of being seen in archeology. • Typically these things can overlap. For example, tools can show things about how bones had to be structured to use them and intelligence to be able to make such tool. 2 of9 Week One and Two 01-11-16 to 01-22-16 “Trends” in Human Evolution 1. Bipedalism • Correlation between locomotive behaviors and bone structure - There are also correlations of the bone structure characteristics within an Order - Homo Sapiens and Pantrogodytes (chimps) • Our Foramen Magnum (the hole in cranium where the spine meets the cranium) is more at the bottom or base of the cranium than it is in chimps. - This can serve as an indicator for posture - with it at the base the head will be held more directly above the spine rather than out in front of it. - This is believed to be one reason for Basicranial flexion (how the cranium is flexed/bent). • There is also a difference in our spines compared to a chimp (and other primates). Chimps Spine: Human Spine: The human spine, or S-shaped spine, is better for bipedalism. • Humans have wide hips and narrow knees, where as the chimp have narrow hips. • Our femurs (thigh bone) have what is called a carrying angle. - The two bumps at the end of the femur (where it meets the other bone in the leg and knee) are at two different levels. Where chimps feet have what is called grasping function (the big toe is • divergent from the others and allows for them to grasp things with it) we 3 of9 Week One and Two 01-11-16 to 01-22-16 have feet with supporting function. This brings the big toe in line with the others and changes the ankle bones causing our feet to have arches. - The arches give us a spring in our step, allowing for more of our energy to be conserved rather than be dispersed into the ground and lost. 2. Exploiting a terrestrial environment There are three aspects of this • 1. The sexual division of labor 2. K-Selection - This is a reproductive strategy - one of two. K-Selection means there are fewer offspring, but the parents are invested in the offsprings wellbeing. - The other is R-Selection which is many offspring, but little or no investment by the parents. 3. Language - There is some evidence of this in fossil records. - 2 parts of the brain that deals with language 1. Broca’s area is the part of the brain that converts ideas into symbols/language 2. Wernicke’s area is the part that converts language into ideas for us to recognize them. *Note that language doesn’t necessarily mean spoken language. 3. Increase in brain size and complexity • Cranium Endocast: when the skull/cranium fills with sentiment and hardens leaving an imprint or copy of what the inside would look like. Typically grooves and bumps. 4 of9 Week One and Two 01-11-16 to 01-22-16 The human brain size, on average, is 1400 cubic centimeters • - This varies depending on the size of the human. • The is an increase of grooves and folds on the neocortex (responsible for higher thinking) in humans. • Encephalization Quotient (EQ) deals with the brain to body ratio and intelligence. 4. Tool making and object manipulation It is worth noting that chimps can also use materials, say stone, as a tool, but • they cannot modify or manipulate the stone. This seems to be only a human characteristic. - This comes back to the evolution of the hand more than the evolution of the brain. Our hands allow us to practice and have what is called precision grip. - Precision grip: (almost uniquely human): The ability to hold something between the thumb and a finger. - Power grip: (something done by all primates): The ability to wrap hand/fingers around an object • In comparison to chimps, they are stronger than humans in almost every way, but there hands are weak. 5. Increased meat eating (tooth classes) • Four classes, or kinds, of teeth. 1. Incisors 2. Canine 3. Premolar 4. Molar • We tend to have a thicker enamel than african primates • Our teeth wear down flat 5 of9 Week One and Two 01-11-16 to 01-22-16 • Our canines teeth are much smaller than those of primates - Primates have a Diastema (gap) between teeth on the top and bottom rows for the canine teeth to sit comfortably. • Dental Arcade: The upper or lower row of teeth. Only referring to one or the other, not both. - Primates have a U-shape upper arcade. - Humans have a parabolic shape (the teeth diverge from one another). Mosaic Evolution: • Evolution at different rates. - Different parts of the body grow and develop at different times. Some lead to other parts growing and developing. - Think back to the use of tools. The hands developed and were able to manipulate tools, which could have played a part in the growth of the brain (figuring out uses for tools/creation of more). Reconstructing the past: What is a fossil 1. Remains of an ancient organism that is preserved 2. Materialized evidence of past life • Two kinds of fossils: 1. True Fossil: Remains 2. Trace Fossil: Traces or imprints left behind Fossilization: The process that preserves evidence by means of mineralization • What Constitutes a fossil • Typically based on how much of the process is complete, but it depends on who you talk to. 6 o 9 Week One and Two 01-11-16 to 01-22-16 • Influences on fossilization: • Structure of the Environment: Water and Temperature: 1. Water Consistency is important 2. Temperature 3. Shelter and Protection 4. Burial • Structure of the Organism 1. Hardness 2. Size Taphonomy: • Study of an organism after death • Necrology - how it dies/ what the cause of death is • Biostratinomy - Transfer from life to death, but before it is buried • Diagenesis - fossilization once it is buried - Fossil bones can become warped Assemblage: Theoretical Ideals • It is not something we can have or hold • Four Assemblages - Life Assemblage is the totality of all living things at a specific point in time. - Death Assemblage is a subset of life assemblage. It is the totality of all the dead things at a specific point in time. - Preservation Assemblage is a subset of the total death assemblage. 7 of9 Week One and Two 01-11-16 to 01-22-16 - Collection Assemblage is a subset of preservation assemblage. It is the portion brought back to the lab. • This introduces a bias of that which is collected • Collection assemblage is used to reconstruct the preservation assemblage which is used to reconstruct the death assemblage which is used to reconstruct the life assemblage. - We use taphonomy to understand why our collection assemblage is the way it is - why we have the samples we have. • Was something more common, thus we have more or was it living underground which is more likely to be preserved Dating Fossils: • Relative Dating - these are techniques that give the age of something relative to the age of something else. - Stratigraphy - Accumulation of sediments that are layered. - Law of superposition: Says the younger strata’s will be layered above the older strata’s. Thus the older fossils will be below the younger ones. - Biostratigraphy - the ‘life spans’ of species. How long the species survived. - Faunal zones (animal zones) - Land Mammals Age (we live in this age). • Absolute (Chronometric) Dating - These are techniques that give age of something in actual measurements/units of time. - Paleomagnetism - Changes in the Earth’s polarity - Dates from minerals in the - Ocean sediments When the polarity changes you can see the change in the sediments or - lake sediments layers of these. - igneous rocks - ceramics 8 of9 Week One and Two 01-11-16 to 01-22-16 - metals Declination is the difference between true and magnetic north. - Radiometric Techniques - Half-lives is how long it takes for something (class example was potassium and uranium). - Potassiums half-life is 1.3 billion years. • It does not matter the amount, or unit, of the element. It will still take that 1.3 billion (or what ever the time is) to get to the the next half-life. - If you have one unit of potassium it will take 1.3 billion years to get to 1/2 unit. From there it will take another 1.3 billion years to get to 1/4 unit. 9 of9

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Chapter 5.3, Problem 5.1.193 is Solved
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Textbook: Trigonometry
Author: Charles P McKeague
ISBN: 9780495108351

The answer to “Use exact values to show that each of the following is true. sin 60 = 2 sin 30 cos 30” is broken down into a number of easy to follow steps, and 20 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 58 chapters, and 3545 solutions. The full step-by-step solution to problem: 5.1.193 from chapter: 5.3 was answered by , our top Math solution expert on 01/02/18, 08:55PM. Trigonometry was written by and is associated to the ISBN: 9780495108351. This textbook survival guide was created for the textbook: Trigonometry, edition: . Since the solution to 5.1.193 from 5.3 chapter was answered, more than 245 students have viewed the full step-by-step answer.

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Use exact values to show that each of the following is