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Trigonometric Trigonometric ratios


The triangle is the key figure metric description for any surface.
Surveyors in purely practical applications, reduce their problems to triangulations.
The theoretical mathematician, in his analysis, often also used this basic polygon
should consider a number of previous definitions:
• A segment x is the mean proportional between two a, b when checked:
·
· Given a point P ay line is called projection of point P on the line to the point P 'defined as the intersection of the perpendicular drawn from P aa and the same line a.
· Projection of a segment MN is on a straight segment M'N ' whose endpoints are the projections of the ends M, N given segment on the line a.
• In a right triangle, sine of an angle is the ratio (the ratio) between the opposite side and the hypotenuse, the cosine of an angle is the relationship between adjacent and the hypotenuse side, the relationship between the sine and cosine an angle (or equivalently the ratio of opposite and adjacent) is the tangent of that angle.
• Although defined in a right triangle, the values \u200b\u200bof sine, cosine and tangent of an angle are fixed values \u200b\u200bthat are fully tabulated in trigonometric tables.
· The reasons sine (sin), cosine (cos) and tangent (tan) and their inverses: cosecant (cosec = 1/sen), secant (sec = 1/cos) and cotangent (cotg = 1/tg) are called trigonometric ratios.




Be the triangle ABC (rectangle in A)
angle
trigonometric ratio 0 º 30 º 45 º 60 º 90 º
Seno 0 0.5 0.707 0.866 1
Cosine 1 0.866 0.707 0.5 0
Tangent 0 .577 1 1, 73 oo

Theorem: Theorem
leg.
In any right triangle verifies that one leg is a mean proportional between the hypotenuse and the projection of that leg on the hypotenuse:

height theorem.
In any triangle, the height is a mean proportional between the two segments that divides the hypotenuse:

Pythagorean Theorem.
In any right triangle is true that the square of the hypotenuse equals the sum of the squares of the legs:
a2 + b2 = c2
From the definitions of the trigonometric ratios follows:
b = a sin B = a
cos C c = a cos B = a sin C
tg B b = c, c = b tg C