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trigonometric applications trigonometric applications there are an enormous number of uses of trigonometry and trigonometric functions for instance the technique of triangulation is used in astronomy to measure the distance to nearby stars in geography to measure distances between landmarks and in satellite navigation systems the sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves trigonometry is the branch of mathematics which deals with triangles and the relationship between the angles and sides of triangles now we will see some applications of trigonometry sine law ­ the law of sine is also known as sine law sine formula or sine rule is an equation which is used to compare the length of the sides of a triangle to its angle know more about graphing circular functions tutorcircle.com page no 1/4

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trigonometry from greek trignon triangle metron measure 1 is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides trigonometry defines the trigonometric functions which describe those relationships and have applicability to cyclical phenomena such as waves the field evolved during the third century bc as a branch of geometry used extensively for astronomical studies.it is also the foundation of the practical art of surveying trigonometry basics are often taught in school either as a separate course or as part of a precalculus course the trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as fourier analysis and the wave equation which are in turn essential to many branches of science and technology spherical trigonometry studies triangles on spheres surfaces of constant positive curvature in elliptic geometry it is fundamental to astronomy and navigation trigonometry on surfaces of negative curvature is part of hyperbolic geometry if one angle of a triangle is 90 degrees and one of the other angles is known the third is thereby fixed because the three angles of any triangle add up to 180 degrees the two acute angles therefore add up to 90 degrees they are complementary angles the shape of a triangle is completely determined except for similarity by the angles once the angles are known the ratios of the sides are determined regardless of the overall size of the triangle read more about hyperbolic trigonometric functions tutorcircle.com page no 2/4

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if the length of one of the sides is known the other two are determined these ratios are given by the following trigonometric functions of the known angle a where a b and c refer to the lengths of the sides in the accompanying figure the hypotenuse is the side opposite to the 90 degree angle in a right triangle it is the longest side of the triangle and one of the two sides adjacent to angle a the adjacent leg is the other side that is adjacent to angle a the opposite side is the side that is opposite to angle a the terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively many english speakers find it easy to remember what sides of the right triangle are equal to sine cosine or tangent by memorizing the word sohcah-toa see below under mnemonics tutorcircle.com page no 3/4 page no 2/3

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thank you for watching presentation

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