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TRIGONOMETRY
FUNCTIONS  AND  COFUNCTIONS

Engineering Aid 3 - Beginning Structural engineering guide book
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Figure 1-19.-Generation of an angle, resulting angle measured  in  degrees. 90° sectors, called QUADRANTS, are numbered counterclockwise  starting  at  the  upper  right-hand sector. When the unit radius r (the line generating the angle)  has  traveled  less  than  90°  from  its  starting point   in   a   counterclockwise   direction   (or,   as conventionally   referred   to   as,   in   a   positive direction),  the  angle  is  in  the  FIRST  quadrant  (I). When the unit radius lies between 90° and 180°, the angle is in the SECOND quadrant (II). Angles between  180°  and  270°  are  said  to  lie  in  the THIRD  quadrant  (III),  and  angles  greater  than 270°  and  less  than  360°  are  in  the  FOURTH quadrant  (IV). When  the  line  generating  the  angle  passes through more than 360°, the quadrant in which the  angle  lies  is  found  by  subtracting  from  the angle the largest multiple of 360 that the angle contains and determining the quadrant in which the remainder falls. The  RADIAN  SYSTEM  of  measuring  angles is even more fundamental than the degree system. It  has  certain  advantages  over  the  degree  system, for it relates the length of arc generated to the size of the angle and the radius. The radian measure is shown in figure 1-20. If the length of the arc (s) described by the extremity of the line segment generating the angle is equal to the length of the line (r), then it is said that the angle described is exactly equal to one radian in size; that is, for one radian,  s  =  r. The circumference of a circle is related to the radius  by  the  formula,  C  =  2nr.  This  says  that the  circumference  is  2rt times the length of the radius.  From  the  relationship  of  arc  length, radius, and radians in the preceding paragraph, this  could  be  extended  to  say  that  a  circle Figure 1-20.-Radian measure. Figure 1-21.-Circle of unit radius with quadrants shown. contains   2rr   radians,    and  the  circumference encompasses  3600  of  rotation.  It  follows  that By dividing both sides of the above equation by  n,  we  find  that As  in  any  other  formula,  you  can  always convert radians to degrees or vice versa by using the  above  relationship. FUNCTIONS  OF  ANGLES The  functions  of  angles  can  best  be  illustrated by means of a “circle of unit radius” like the one shown in figure 1-21. A so-called “Cartesian axis” 1-17







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