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Math Review of the Law of Cosines 150 150 Deborah

Math Review of the Law of Cosines

Overview The Law of Cosines is true because of properties of any triangle, not just right triangles. In fact, the Pythagorean Theorem is a special case of the Law of Cosines. The Law of Cosines and the Law of Sines can be used together to solve triangles with trigonometric ratios, if enough facts are known…

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Math Review of the Law of Sines 150 150 Deborah

Math Review of the Law of Sines

Overview Some of the properties of a triangle hold true even if it is an oblique triangle, when none of the angles are right angles. We can solve the sides and angles of other triangles by using trigonometric ratios, as long as we have enough information. What Information Is Necessary? Any triangle has 6 pieces of…

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Math Review of Circular Functions 150 150 Deborah

Math Review of Circular Functions

Overview The trigonometric functions can also be defined in terms of the unit circle, so sometimes they are called the circular functions. This is because of the relationships of the trigonometric functions of angles to the unit circle. The trigonometric functions correspond to coordinates on the unit circle, also called terminal points. Trigonometric Functions as…

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Math Review of Arcs and the Unit Circle 150 150 Deborah

Math Review of Arcs and the Unit Circle

Overview One of the methods of measuring angles is to measure them in relationship to a unit circle and as the measurement of an arc. Applications include periodic behavior such as light, sound or other waves along the electronic spectrum, and the processing of signals. The Unit Circle Suppose that a circle is constructed from a…

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Science Review: Do Planets Exist in Other Star Systems? 150 150 Deborah

Science Review: Do Planets Exist in Other Star Systems?

Overview: From the time that Galileo and other astronomers observed that some stars were double, scientists have been fascinated with the thought that stars other than the sun might have planets that orbit them. The most recent discoveries by the Hubble and the Kepler Space Telescopes suggest that planets may be more common in the universe than…

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Science Review of Multiple Star Systems 150 150 Deborah

Science Review of Multiple Star Systems

Overview Although the star we are most familiar with exists as a single star, many common stars exist in pairs or multiple star systems. More than half of all stars are possibly multiple, deduced from observations of their spectra and motion. They are bound by mutual gravitational attraction, and orbit around common points. Some stars…

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Science Review of Comets 150 150 Deborah

Science Review of Comets

Overview Comets are small icy rocks that belong to the solar system. Many have highly elliptical orbits that pass close to the sun. As they heat, they begin to vaporize, forming a tail of gases and dust. Many comets, such as Halley’s Comet, are regular and predictable, and have been the sources of legends throughout…

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Science Review of the Main Sequence, Red Giants, and Supergiants 150 150 Deborah

Science Review of the Main Sequence, Red Giants, and Supergiants

Overview According to theories of stellar evolution, most stars spend most of the time converting hydrogen to helium in various nuclear processes. After the supply of hydrogen is exhausted in the stellar core, most stars begin using helium for nuclear fuel. The largest stars use helium as well as other elements for nuclear fusion. The Main…

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Science Review of Stellar Structure and Nuclear Reactions inside Stars 150 150 Deborah

Science Review of Stellar Structure and Nuclear Reactions inside Stars

Overview The nuclear energy that powers stars depends upon the core temperature and the available fuel. During the main-sequence phase for most stars, nuclear fusion of 4 hydrogen atoms to form 2 helium atoms provides the most energy. Other types of fusion reactions occur in stars with higher core temperatures and when hydrogen fuel is…

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Science Review of White Dwarfs, Neutron Stars, and Black Holes 150 150 Deborah

Science Review of White Dwarfs, Neutron Stars, and Black Holes

Overview When hydrogen fuel is exhausted within a stellar core, rapid changes take place within the star depending upon its mass and temperature. Some of these nuclear reactions result in a stellar explosion and collapse. As all nuclear fuel is exhausted, matter is compressed into white dwarfs, black holes, and other cosmic variations. Structure of…

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