Geo5.4.6

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Find the area of the triangle formed by the points (1,{\frac  {\pi }{6}}),(2,{\frac  {\pi }{3}}),(3,{\frac  {\pi }{2}})\,

The area of the triangle is

{\frac  {1}{2}}[(1)(2)\sin {\frac  {\pi }{6}}-{\frac  {\pi }{3}}+(2)(3)\sin {\frac  {\pi }{3}}-{\frac  {\pi }{2}}+(3)(1)\sin {\frac  {\pi }{2}}-{\frac  {\pi }{6}}]\,

{\frac  {1}{2}}[-2\sin {\frac  {\pi }{6}}-6\sin {\frac  {\pi }{6}}+3\sin {\frac  {\pi }{3}}]\,

{\frac  {1}{2}}[-2({\frac  {1}{2}})-6{\frac  {1}{2}}+3{\frac  {{\sqrt  {3}}}{2}}]\,

{\frac  {1}{2}}[-1-3+{\frac  {3{\sqrt  {3}}}{2}}]\,

{\frac  {1}{4}}[-8+3{\sqrt  {3}}]\,


Main Page:Geometry:Polar Coordinates