Step 1Heat the oven to 325 degrees. Set aside an ungreased 10-inch tube pan.
Step 2Sift the flour, baking powder, sugar and salt together into a bowl. Make a well and add the oil, egg yolks, water and vanilla and almond extracts. Beat with a spoon until smooth, or mix with an electric mixer on medium speed, 1 minute.
Step 3Place the egg whites and cream of tartar in a bowl and beat with an electric mixer until stiff peaks form, 3 to 5 minutes. Do not under-beat. Gradually pour the yolk mixture over the beaten whites, folding just until blended. Do not stir. Fold in the coconut. Pour the batter into the pan.
Step 4Bake the cake 55 minutes, then increase the temperature to 350 degrees and bake until the cake springs back when touched, 10 to 15 minutes. Turn the pan upside down and place over the neck of a funnel or bottle to cool.
Step 1Combine the sugar, corn syrup and water in a small heavy saucepan. Insert a candy thermometer and partly cover the pan. Bring to a boil over medium heat. Remove the lid and boil without stirring until a drop on the tip of a spoon will spin a 6-to 8-inch thread, or the thermometer registers 240 to 242 degrees.
Step 2Just before the syrup reaches the proper temperature, beat the egg whites with an electric mixer until soft peaks form, 2 to 3 minutes. When the syrup reaches the correct temperature, set the mixer at high speed and pour the syrup into the whites in a slow thin stream. Beat until glossy and firm enough to hold their shape, 3 to 4 minutes. Beat in the vanilla.
Step 1Loosen the sides of the cake from the pan with a spatula and remove from the pan. Cut the cake in half using a serrated knife to make 2 layers. Fill the cake with about 1/4 of the frosting, then replace the top layer. Frost the top and sides with the remaining frosting. Sprinkle generously with the coconut.