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Intro Math Plane trigonometry by Loney

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  1. Feb 1, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Part I
    [LIST]
    [*] Measurement of angles. Sexagesimal and Centesimal Measure
    [*] Circular, or Radian, Measure
    [*] Trigonometrical Ratios for angles less than a right angle
    [*] Values for angles of 45°, 30°, 60°, 90° and 0°
    [*] Simple problems in Heights and Distances
    [*] Applications of algebraic signs to Trigonometry
    [*] Tracing the changes in the ratios
    [*] Trigonometrical ratios of angles of any size. Ratios for -\theta ,90°-\theta,90°+\theta,...
    [*] General expressions for all angles having a given trigonometrical ratio
    [*] Ratios of the sum and difference of two angles
    [*] Product Formulae
    [*] Ratios of multiple and submultiple angles
    [*] Explanation of ambiguities
    [*] Angles of 18°, 36°, and 9°
    [*] Identities and trigonometrical equations
    [*] Logarithms
    [*] Tables of logarithms
    [*] Principle of Proportional Parts
    [*] Sides and Angles of a triangle
    [*] Solution of triangles
    [*] Given two sides and the included angle
    [*] Ambiguous Case
    [*] Heights and Distances
    [*] Properties of a triangle
    [*] The circles connected with a triangle
    [*] Orthocentre and Pedal triangle
    [*] Centroid and Medians
    [*] Quadrilaterals
    [*] Regular Polygons
    [*] Trigonometrical ratios of small angles. sin \theta < \theta <tan \theta
    [*] Area of a Circle
    [*] Dip of the horizon
    [*] Inverse circular functions
    [*] Some simple trigonometrical Series
    [*] Elimination
    [/LIST]
    [*] Analytical Trigonometry
    [LIST]
    [*] Exponential and Logarithmic Series
    [*] Logarithms to base e
    [*] Two important limits
    [*] Complex quantities
    [*] De Moivre's Theorem
    [*] Binomial Theorem for complex quantities
    [*] Expansions of sin n\theta, cos n\theta, and tan n\theta
    [*] Expansions of sin a and cos a in a series of ascending powers of a
    [*] Sines and Cosines of small angles
    [*] Approximation to the root of an equation
    [*] Evaluation of indeterminate quantities
    [*] Expansions of cos^n \theta and sin^n \theta in cosines or sines of multiples of \theta
    [*] Expansions of sin n\theta and cos n\theta in series of descending and ascending powers of sin \theta and cos \theta
    [*] Exponential Series for Complex Quantities
    [*] Circular functions of complex angles
    [*] Euler's exponential values
    [*] Hyperbolic Functions
    [*] Inverse Circular and Hyperbolic Functions
    [*] Logarithms of complex quantities
    [*] Value of a^x when a and x are complex
    [*] Gregory's Series
    [*] Calculation of the value of \pi
    [*] Summation of Series
    [*] Expansions in Series
    [*] Factors of x^{2n} - 2x^n cos n\theta + 1
    [*] Factors of x^n - 1 and x^n + 1
    [*] Resolution of sin \theta and cos \theta into factors
    [*] sinh \theta and cosh \theta in products
    [*] Principle of Proportional Parts
    [*] Errors of observation
    [*] Miscellaneous Propositions
    [*] Solution of a Cubic Equation
    [*] Maximum and Minimum Values
    [*] Geometrical representation of complex quantities
    [*] Miscellaneous Examples
    [/LIST]
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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