Cream butter, sugar, baking soda and cream of tartar together. Add egg and vanilla and beat well. Combine cocoa with flour. Beat as much of the flour mixture as you can with an electric mixer. Stir in any remaining flour mixture. Drop by rounded teaspoonfulls two inches apart on ungreased cookie sheets. Stir together remaining sugar and cinnamon and sprinkle on dough. Bake at 375 degrees for 9 to 11 minutes or until edges are firm.