ANSWERS: 2
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The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere. http://encarta.msn.com/encyclopedia_761572350/Trigonometry.html
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1.)Rational trigonometry 2.)Spherical trigonometry http://en.wikipedia.org/wiki/List_of_basic_trigonometry_topics#Branches_of_trigonometry
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