You cost basis in the home will be based on the appraisal done.
Assets that were owned by someone who passed away can be revalued as of the date of death. Since you had an appraisal done, you know what that value was. At the time, your basis was 1/2 of the appraised value. When you purchased your sister's interest in the house, your basis was increased by the amount that you paid (so your basis was then 100% of the appraised value).
You basis may have increased if you have made any improvements to the house - the cost of these would be added to your basis.
