Artículos relacionados a Elementary text-book of trigonometry
Sinopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 edition. Excerpt: ... therefore, in determining the value of sinA from the value of cosA, we get, in general, two equal values of opposite sign. If we know in what quadrant A lies, we know whether sinA is positive or negative, and there is no ambiguity. The reason of the ambiguity can easily be assigned. By Arts. 41 and 46, the cosine of the angle A and the cosine of the angle 360-A are equal numerically and have the same algebraical sign, while the sine of the angle A and the sine of the angle 360-A are equal numerically but have opposite algebraical signs. Hence, in determining the value of the sine of A from the value of the cosine of A, we might expect to get two equal values of opposite sign, the one value being the sine of A and the other value the sine of 360-A. Similar remarks apply to the equations cosA = + Vl-sin2A, secA= + VI +tan2A, &c. 49. Changes in sinA as the Angle A increases from 0 up to 360. Let A denote the angle AOP described by the revolution of OP about the fixed end O from the initial position O A. Then, PM being drawn perpen., dicular to AA', PM sinA = whatever be the magnitude of the angle A. When the angle A is zero, P coincides with A, or PM is zero, and therefore sin0=0. As the angle increases PM increases until the angle becomes a right angle, and then PM is equal to OB or OP, and therefore as the angle A increases from 0 up to 90, sinA increases from 0 up to 1. When the angle A becomes greater than a right angle PM diminishes; this continues until the angle A is an angle of two right angles or 180, and then OP coincides with OA' or PM is zero. Hence as A increases from 90 up to 180, sinA diminishes from 1 down to 0. When the angle A becomes greater than 180, PM becomes negative and begins to increase. This increase continues until...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 edition. Excerpt: ... therefore, in determining the value of sinA from the value of cosA, we get, in general, two equal values of opposite sign. If we know in what quadrant A lies, we know whether sinA is positive or negative, and there is no ambiguity. The reason of the ambiguity can easily be assigned. By Arts. 41 and 46, the cosine of the angle A and the cosine of the angle 360-A are equal numerically and have the same algebraical sign, while the sine of the angle A and the sine of the angle 360-A are equal numerically but have opposite algebraical signs. Hence, in determining the value of the sine of A from the value of the cosine of A, we might expect to get two equal values of opposite sign, the one value being the sine of A and the other value the sine of 360-A. Similar remarks apply to the equations cosA = + Vl-sin2A, secA= + VI +tan2A, &c. 49. Changes in sinA as the Angle A increases from 0 up to 360. Let A denote the angle AOP described by the revolution of OP about the fixed end O from the initial position O A. Then, PM being drawn perpen., dicular to AA', PM sinA = whatever be the magnitude of the angle A. When the angle A is zero, P coincides with A, or PM is zero, and therefore sin0=0. As the angle increases PM increases until the angle becomes a right angle, and then PM is equal to OB or OP, and therefore as the angle A increases from 0 up to 90, sinA increases from 0 up to 1. When the angle A becomes greater than a right angle PM diminishes; this continues until the angle A is an angle of two right angles or 180, and then OP coincides with OA' or PM is zero. Hence as A increases from 90 up to 180, sinA diminishes from 1 down to 0. When the angle A becomes greater than 180, PM becomes negative and begins to increase. This increase continues until...
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