Docstoc

Formulas and computations

Document Sample
Formulas and computations Powered By Docstoc
					Formulas and computations:
Be able to compute/note down the formulas for if needed:

      The relationships between central angle and minor/major arc on p 196, and
       additivity of arc measure (be able to fill in angle/arc measures on a circle and give
       a brief justification). Most of the computational formulas for these relationships
       appear later on; this is just the initial definitions.
      Calculating the defect for triangles in hyperbolic geometry (difference of angle
       sum from 180). Calculating the area for triangles in hyperbolic geometry (
              
       A           ).
                180
      Finding the equation of a line in hyperbolic geometry (general equation:
        x 2  y 2  ax  by  1 , use given ( x, y ) pairs to solve for a and b ) .
                                                                                     AM  BN
      Finding the length of a segment in hyperbolic geometry: AB*  ln(                     ).
                                                                                     AN  BM
      Using the various parallel line transversal theorems to calculate or solve for angle
       measures in a "parallel lines + transversal" set up. Plus the triangle sum of angles
       theorem for Euclidean geometry.
      Computations using the Midpoint Connector Theorems (p 218 for triangles, p 228
       for trapezoids) – gives result that a midpoint connector (median) crosses the sides
       at the midpoints, is parallel to the base(s), and the formula for the length of the
       median of a trapezoid.
      Using the proportions set up by the Side-Splitting Theorem to calculate side
       lengths in triangles and trapezoids.
                                                                                       1
      The arc/angle relationships in 4.5 (Inscribed Angle Theorem: m A  x where
                                                                                       2
           A is an inscribed angle and x is the measure of the intercepted arc, and all the
                                           1                    1                   1
       variant cases on p272: m A  ( x  y), m A  ( x  y), m A  x (tangent) )
                                           2                    2                   2
      Two-Chord Theorem: AP  PB  CP  PD .
      Secant-Tangent Theorem: PC 2  PA  PB .
      Two-Secant Theorem: PA  PB  PC  PD . For the previous three, be sure you
       know what segments those refer to (make sketches)
      Areas of basic plane figures (on formula sheet); combining into more complex
       figures.
      Using similar triangles to set up proportions and solve for side lengths.
      Volumes and surface areas of basic solids. You do not need to know the formulas
       for the Platonic solids.
                                                           1
      Length of arc L  r and area of sector A  r 2 .
                                                           2
      Law of sines and law of cosines.
   How find a vector given coordinate points. Addition of vectors. Finding x and y
    components of vectors given magnitude and angle, and vice versa. Calculating the
    length (norm, magnitude) of a vector, and finding a unit vector.
   Using direction cosines to find the angle that a vector in 3D makes with x, y, and
    z axes.
   Dot product formula ( u  v  u1v1  u2v2  u3v3 ), and formula for finding angle
                                                 uv
    between two vectors (   cos 1 (                      ) ).
                                            || u || || v ||
                                               v
   How to normalize a vector ( u                  ) and find a vector in the direction of a given
                                            || v ||
                        v
    vector ( || w ||         gives a vector in the direction of v having the length of w ).
                     || v ||
   Euclidean regular polygon computations:
        o Sum of vertex angles: 180(n  2) , measure of each angle that sum divided
            by n .
                                                        360
        o Measure of central angle always
                                                          n
        o Apothem: .5s cot  , where  is half the measure of the central angle, s is
            side length.
        o Perimeter: ns
        o Area: .5asn

   Non-Euclidean polygon computations:
       o Difference between actual angle sum and Euclidean sum is defect
                                       
        o Area computed from               
                                     180

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:9/8/2012
language:English
pages:2