Preheat the oven to 325 degrees F (165 degrees C).
Combine flour, sugar, baking powder, and salt in a mixing bowl. Make a well in the center of the flour mixture and add egg yolks, water, oil, vanilla extract, and almond extract. Beat until smooth.
Beat egg whites and cream of tartar in a large bowl until stiff peaks form. Pour egg yolk mixture gradually over beaten egg whites and fold until just blended. Fold in flaked coconut. Pour batter into an ungreased 10-inch tube pan.
Bake in the preheated oven for 55 minutes. Increase the oven temperature to 350 degrees F (175 degrees C) and bake for 10 to 15 minutes longer. Top will spring back when touched lightly. Turn the pan upside down until cake is cool before removing from the pan. Remove cooled cake from pan and frost if desired.