MATH 182A Lecture 13: 10.3_polar-coordinates
Document Summary
Instead of an x,y coordinate, polar coordinates are de ned by an angle and a radius. 270 285 x = r cos( ) y = r sin( ) 1 y (r, ) x ( r, ) or (r, + ) Shade the region 1 r 2. y x. Find the distance between the two points: y (r2, 2) (r1, 1) x. P1(x1, y1) p2(x2, y2) x1 = r1 cos( 1) x2 = r2 sin( 2) y1 = r1 sin( 1) y2 = r2 sin( 2) = p(r2 cos( 2) r1 cos( 1))2 + (r2 sin( 2) r1 sin( 1))2. = q(r2)2 cos2( 2) + (r1)2 cos2( 1) + (r2)2 sin2 2 + (r1)2 sin2( 1) 2r1r2 sin( 1) sin( 2) = p(r1)2 + (r2)2 2r1r2 cos( 1 2) (law of cosines) We could also have drawn a triangle and applied the law of cosines, but this shows a the derivation of the law.
