MATHEMATICS   Formulas, Graphs, Tables, . . .  < High School to University Level >
CONTENTS E
 41  Applications of trigonometry
      Mollweide's formulas, the tangent law (or the tangent rule) and half-angle formulas
         Oblique or scalene triangle - Mollweide's formulas
         Oblique or scalene triangle - The tangent law (or the tangent rule)
         Oblique or scalene triangle - Half-angle formulas
      Area of a triangle, the radius of the circumscribed circle and the radius of the inscribed circle
         The area of a triangle in terms of an angle and the sides adjacent to it
         The area of a triangle in terms of a side and all its angles
         The radius of the circumscribed circle or circumcircle
         The area of a triangle in terms of the radius of circumcircle and all its angles
         The area of a triangle in terms of the inscribed circle (or incircle) radius, Heron's formula
         Oblique or scalene triangle examples
 42  Applications of trigonometry in plane geometry
         The parallelogram, area of a parallelogram
      Trapezoid or trapezium
         The area of a trapezoid given its four sides
         The area of the trapezoid given two parallel sides and angles at ends of the side
         Diagonals of a trapezoid given its four sides
         Applications of trigonometry in solid geometry
         A right pyramid and regular right pyramid
      Sections of solids
         Sections of solids examples
 43  Oblique prism
         Oblique pyramid
      Volume and surface area of solids of revolution, Guldin’s rules
         Applications of trigonometry in geodesy (or plane surveying)
         Applications of trigonometry in geodesy examples
         Applications of trigonometry in physics
         Applications of trigonometry in physics examples
 44  Trigonometry
      Trigonometric functions
         Unit of measurement of angles - a radian (the circular measure)
         The unit circle or trigonometric circle
         Division of the circumference of the unit circle to the characteristic angles
         Definitions of trigonometric functions
         Periodicity of trigonometric functions
         Signs of trigonometric functions
         Trigonometric functions of negative arcs or angles
      Trigonometric functions of arcs from  0 to ± 2p
         Trigonometric functions of negative arcs or angles
         Trigonometric functions of complementary angles
         Trigonometric functions of supplementary angles
         Trigonometric functions of arcs that differ on p/2
         Trigonometric functions of arcs that differ on p
         Trigonometric functions of arcs whose sum is 2p
 45  Trigonometric functions of arcs from 0 to ± 2p
         Values of trigonometric functions of arcs p/6, p/4 and p/3
         The values of the trigonometric functions of arcs that are multipliers of 30° (p/6) and 45° (p/4)
      Calculation of values of trigonometric functions
         Trigonometric reduction formulas - the reference angles
         Calculation of values of trigonometric functions of an arbitrary angle x, examples
      Basic relationships between trigonometric functions of the same angle
         Basic relationships between trigonometric functions of the same angle shown in the unit circle
         Basic relationships between trigonometric functions shown in the tabular form
         Trigonometric expressions examples
 46  The addition formulas and related identities
         Deriving the addition formulas for sine and cosine functions
         The addition formulas for tangent and cotangent functions
         Trigonometric functions of double angles, double angle formulas
         Trigonometric functions expressed by the half angle
         Trigonometric functions of double angles expressed by the tangent function
         Trigonometric functions expressed by the tangent of the half angle
         Half angle formulas
         Trigonometric functions expressed by the cosine of the double angle
 47  Sum to product and product to sum formulas or identities
         Sum to product formulas for the sine and the cosine functions
         Sum to product formulas for the tangent and the cotangent functions
         The product to sum formulas for the sine and cosine functions
         Trigonometric identities examples
 48  Trigonometric functions and inverse trigonometric functions or arc-functions
      Trigonometric functions graphs and relations
      The graph of the sine function  f(x) = sin x
         Properties of the sine function
      The graph of the cosine function  f (x) = cos x
         Properties of the cosine function
      The graph of the tangent function  f (x) = tan x
         Properties of the tangent function
      The graph of the cotangent function  f (x) = cot x
         Properties of the cotangent function
         The graph of the function  y = a sin (bx + c)
         The function y = a sin x
         The function y = sin bx
         The function y = sin (x + c)
         The function y = a sin (bx + c)
 49  Inverse trigonometric functions or arc-functions and their graphs
         Inverse functions
      The arc-sine function and the arc-cosine function
         The arc-sine function
         The arc-cosine function
         The graphs of the arc-sine function and the arc-cosine function
      The arc-tangent function and the arc-cotangent function
         The arc-tangent function
         The arc-cotangent function
         The graphs of the arc-tangent function and the arc-cotangent function
      The arc-cosecant function and the arc-secant function
         The arc-cosecant function
         The arc-secant function
         The graphs of the arc-cosecant and the arc-secant function
 50  Trigonometric equations
         Basic trigonometric equations
      The equation  sin x = a,   -1 < a < 1
         The equation  sin x = a example
      The equation  cos x = a,   -1 < a < 1
         The equation  cos x = a example
 
 
 
 
 
 
 
 
 
 
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