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Trigonometry

Math Review of Trigonometry and Navigation

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Overview Trigonometry in the form of triangulation is at the heart of navigation, whether it is by land, sea, or air. GPS systems use triangulation to find and fix positions, extrapolating what is unknown from what is known. Triangulation is also used to measure the distances between earth and distant stars and galaxies, thus aiding…

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The Measurement of Parallax: Angles We Have Seen on High

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Overview The demonstration of parallax is as close as an observer’s own two eyes. It is the measurement of how the same object appears from two different points of view. Astronomers use the very small angles observed by parallax to estimate distances and relative motion of objects ranging from the sun, moon, and planets to…

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Math Review of Platonic Solids and Polyhedra

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Overview There are infinitely many regular polygons. However, there are a fixed number of regular polyhedra, called Platonic solids. Mathematicians use the definitions of the regular polygons and the characteristics of solid objects to arrive at their conclusions. Characteristics of Regular Polyhedra Regular polygons, such as equilateral triangles, squares, equilateral pentagons, hexagons, heptagons, octagons, and…

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Math Review of More Properties of Circular Functions

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Overview The unit circle has as its center the origin point of the Cartesian coordinates x and y, and has a radius 1. The trigonometric functions are also called circular functions, because they describe relationships between angles on the unit circle. We use different ways to describe trigonometry in order to see how the relationships…

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Math Review of Applications of Circular Functions

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Overview Circular trigonometric functions can be applied to situations in physical, biological, and social sciences involving data that follows a pattern that is not linear. Many of those patterns are periodic, and can be modeled by approximations of sine, cosine, or other functions. The Sine and Cosine Waves The numerical value of t around the…

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Math Review of Angles and Circular Motion

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Overview Trigonometry is defined by the measurement of angles and their relationships. One of the ways that trigonometry can be applied is in the measurement of angles and circular motion. Angle Measure Angles in trigonometry and calculus can be measured in radians, which is a relationship of the measurement of an angle by the arc…

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Trigonometry Review of Degrees, Radians, and Measurement of Angles

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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

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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

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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

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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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