Whisk the sugar, corn syrup, cream of tartar, salt, and water together in a small, heavy-bottomed saucepan. Bring to a boil over medium heat (do not stir it) and cook, undisturbed, until it reaches 240°F on a candy thermometer, about 2 minutes; stirring can cause the sugar to crystallize.

Meanwhile, in a medium bowl using an electric mixer on high speed, beat the egg whites until foamy.

Once the sugar syrup reaches 240°F, immediately and carefully pour it into the egg whites, with the mixer running on high speed, away from the beaters to prevent splattering and possible burns. Continue to beat until the frosting is glossy and fluffy, about 5 minutes. Beat in the coconut extract. Use immediately.