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trigonometrical

trigonometrical

 

  2  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Trigonometric  \Trig`o*no*met"ric\,  Trigonometrical 
  \Trig`o*no*met"ric*al\,  [Cf.  F.  trigonom['e]trique.] 
  Of  or  pertaining  to  trigonometry;  performed  by  the  rules  of 
  trigonometry.  --{Trig`o*no*met"ric*al*ly},  adv 
 
  {Trigonometrical  curve},  a  curve  one  of  whose  co["o]rdinates 
  is  a  trigonometric  function  of  the  other 
 
  {Trigonometrical  function}.  See  under  {Function}. 
 
  {Trigonometrical  lines},  lines  which  are  employed  in  solving 
  the  different  cases  of  plane  and  spherical  trigonometry, 
  as  sines,  tangents,  secants,  and  the  like  These  lines,  or 
  the  lengths  of  them  are  trigonometrical  functions  of  the 
  arcs  and  angles  to  which  they  belong. 
 
  {Trigonometrical  survey}.  See  under  {Survey}. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
 
 
  Note:  Co["o]rdinates  are  of  several  kinds,  consisting  in  some 
  of  the  different  cases,  of  the  following  elements, 
  namely: 
  a  (Geom.  of  Two  Dimensions)  The  abscissa  and  ordinate  of 
  any  point,  taken  together;  as  the  abscissa  PY  and 
  ordinate  PX  of  the  point  P  (Fig.  2,  referred  to  the 
  co["o]rdinate  axes  AY  and  AX 
  b  Any  radius  vector  PA  (Fig.  1),  together  with  its  angle 
  of  inclination  to  a  fixed  line  APX,  by  which  any 
  point  A  in  the  same  plane  is  referred  to  that  fixed 
  line  and  a  fixed  point  in  it  called  the  pole,  P. 
  c  (Geom.  of  Three  Dimensions)  Any  three  lines,  or 
  distances,  PB  PC  PD  (Fig.  3),  taken  parallel  to 
  three  co["o]rdinate  axes,  AX  AY  AZ  and  measured 
  from  the  corresponding  co["o]rdinate  fixed  planes, 
  YAZ,  XAZ,  XAY,  to  any  point  in  space,  P,  whose 
  position  is  thereby  determined  with  respect  to  these 
  planes  and  axes. 
  d  A  radius  vector,  the  angle  which  it  makes  with  a  fixed 
  plane,  and  the  angle  which  its  projection  on  the  plane 
  makes  with  a  fixed  line  line  in  the  plane,  by  which 
  means  any  point  in  space  at  the  free  extremity  of  the 
  radius  vector  is  referred  to  that  fixed  plane  and 
  fixed  line  and  a  fixed  point  in  that  line  the  pole 
  of  the  radius  vector. 
 
  {Cartesian  co["o]rdinates}.  See  under  {Cartesian}. 
 
  {Geographical  co["o]rdinates},  the  latitude  and  longitude  of 
  a  place  by  which  its  relative  situation  on  the  globe  is 
  known  The  height  of  the  above  the  sea  level  constitutes  a 
  third  co["o]rdinate. 
 
  {Polar  co["o]rdinates},  co["o]rdinates  made  up  of  a  radius 
  vector  and  its  angle  of  inclination  to  another  line  or  a 
  line  and  plane;  as  those  defined  in 
  b  and 
  d  above. 
 
  {Rectangular  co["o]rdinates},  co["o]rdinates  the  axes  of 
  which  intersect  at  right  angles. 
 
  {Rectilinear  co["o]rdinates},  co["o]rdinates  made  up  of  right 
  lines.  Those  defined  in 
  a  and 
  c  above  are  called  also  {Cartesian  co["o]rdinates}. 
 
  {Trigonometrical}  or  {Spherical  co["o]rdinates},  elements  of 
  reference,  by  means  of  which  the  position  of  a  point  on 
  the  surface  of  a  sphere  may  be  determined  with  respect  to 
  two  great  circles  of  the  sphere. 
 
  {Trilinear  co["o]rdinates},  co["o]rdinates  of  a  point  in  a 
  plane,  consisting  of  the  three  ratios  which  the  three 
  distances  of  the  point  from  three  fixed  lines  have  one  to 
  another.