TrigonometrySpringer Science & Business Media, 2001. gada 8. jūn. - 229 lappuses In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers. |
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acute angle addition formulas adjacent leg altitude Analytic Continuation answer approximately arcsin arcsin(sin arctan calculator central angle Chapter chord circle of radius cos(x cos² cota definition degree measure diagonals diagram below shows Draw the graph equal Example Exercises expression find the numerical given Hint hypotenuse inscribed angle integer inverse function law of cosines Law of Sines line segment linear combination numerical value obtuse angle period Principle of Analytic proof prove Ptolemy's theorem Pythagorean theorem quadrant quadrilateral radian measure ratio real numbers result right angle right triangle rotation sequences of solutions shift sin x sin(a sin(x sin² sine and cosine sinusoidal curves sinx Solve the equation square statement subtends Suppose tan² tangent three angles triangle ABC triangle with sides trigonometric functions units wheel write x-axis π 2π