"Plane trigonometry" is a branch of mathematics that focuses on the relationship between the sides and angles of a triangle. Plane trigonometry builds upon the basic concepts of Euclidean geometry, and it has applications in a variety of mathematical fields, from physics to advanced calculus.
Continue ReadingCelestial navigator Eric DeMan explains that plane trigonometry examines the vertices of a triangle and the surfaces of the planes that cover its three unique sides. Since triangles are composed of straight lines, understanding the relationship between the angles that make up a triangle is essential to understanding plane trigonometry.
The Encyclopaedia Britannica further defines plane trigonometry as an attempt to deduce the remaining sides of a triangle from the sides that are known. While this may seem like the definition of trigonometry, plane trigonometry takes the concept to a higher level of understanding. Traditional geometry only explains the nature of triangles that follow the basic rules of the Euclidean plane. Plane trigonometry goes beyond the Euclidean plane, explaining the nature of more complex relationships between triangles. Plane trigonometry works entirely through logic and deduction, inferring one set of facts about a given triangle based on what is known about the triangle's other angles, vertices and planes.
Learn more about TrigonometryTrigonometry is important to mathematics as an element of calculus, statistics and linear algebra. Outside of mathematics, it is important to physics, engineering, geography and astronomy as well as architectural design.
Full Answer >The law of sines states that, for any given triangle, the ratio of the length of a side divided by the sine of the opposite angle is equal to the same ratio of the other two sides and angles. The law of sines is part of trigonometry.
Full Answer >The law of tangents states that for a triangle with sides a, b and c and corresponding angles A, B and C, (a - b)/(a + b) is equal to the tangent of (1/2[A - B])/(1/2[A + B]).
Full Answer >The ancient Greeks were the first to develop the conceptual framework of trigonometry. The noted Greek astronomers Hipparchus, Menelaus and Ptolomy contributed in advancing the field.
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