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Trigonometry Review of Degrees, Radians, and Measurement of Angles 150 150 Deborah

Trigonometry Review of Degrees, Radians, and Measurement of Angles

Overview Although many students are most familiar with the measurement of angles by degrees, there are other ways to measure angles. In calculus, advanced trigonometry, and applications of calculus to science, angles are measured in radians. The grad is a unit of angle measure used in surveying and as part of the metric system, and…

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Math Review of Trigonometric Identities 150 150 Deborah

Math Review of Trigonometric Identities

Overview Trigonometric identities are relationships between trigonometric ratios that define them in terms of one another. They can be used to help solve problems that involve trigonometric functions. Reciprocal Identities The reciprocal function to the sine is the cosecant, to the cosine is the secant, and to the tangent is the cotangent. In math language,…

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Trigonometry Review of Right Triangles 150 150 Deborah

Trigonometry Review of Right Triangles

Overview Right triangles have special properties that are important to determine trigonometric ratios, such as sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). Those ratios reflect the relationships between the opposite and adjacent angles of the right angle with the hypotenuse. Trigonometric Ratios Suppose a right triangle has an angle…

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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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