Geo5.4.2

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What are the cartesian coordinates of the points

 i). (3,{\frac  {\pi }{6}})\,
 ii). (4,{\frac  {\pi }{3}})\,

i). Given (3,{\frac  {\pi }{6}})\,

r=3,\theta ={\frac  {\pi }{6}}\,

x=r\cos \theta =3\cos {\frac  {\pi }{6}},y=3\sin {\frac  {\pi }{6}}\,

x={\frac  {3{\sqrt  {3}}}{2}},y={\frac  {3}{2}}\,

Hence the cartesian coordinates are ({\frac  {3{\sqrt  {3}}}{2}},{\frac  {3}{2}})\,

ii). Given (4,{\frac  {\pi }{3}})\,

r=4,\theta ={\frac  {\pi }{3}}\,

x=4\cos {\frac  {\pi }{3}}=4({\frac  {1}{2}}),y=4\sin {\frac  {\pi }{3}}=4({\frac  {{\sqrt  {3}}}{2}})\,

x=2,y=2{\sqrt  {3}}\,

Therefore the cartesian coordinates are (2,2{\sqrt  {3}})\,


Main Page:Geometry:Polar Coordinates