Preheat oven to 350 degrees. In a smaller bowl, mix together flour, cream of tartar, baking soda, and salt. Set aside. With your mixer, cream together sugars and butter. Add egg and vanilla, mix. Gradually mix in dry ingredients. Chill dough for at least an hour or 2. I like using a scoop for these cookies, so they are all the same size. Scoop or shape dough into balls. Roll each ball in sugar to coat. Place on a cookie sheet, flatten slightly with hand. Bake 8-10 minutes. If you prefer crisp cookies, leave them in the oven a bit longer. Remove from baking sheet, cool completely on rack before frosting.