The apple, the banana...

Some authorities insist that there is more reduction before words beginning with consonants than there is before words beginning with vowels. The is said to be pronounced /thuh/ before consonants, /thee/ before vowels... If　this distinction is really widely observed in practice, the usage must be dialectal or occur under relatively formal circumstances. A great many well-educated native speakers of English are quite comfortable pronouncing the as /thI/... in all unstressed position.

Prator and Robinett (2002). Manual of American English Pronounciation (4th Ed), Heinle & Heinle Publishing Company: Cambridge, MA

This is the Swedish athelete I was talking about.

English teachers in Japan have a tendency to be strict between the two pronounciations of "the" according to following words. However, as I quoted above, you don't have to be too strict. Anyway, most of picky Japanese teachers pronounce /za/ and /zee/ for "the," which is not correct.

This is the American athelte I was talking about.

日本人英語教師の中には，the の発音が，次に続く単語が母音か子音かによって機械的に変わると信じ込んでいる人が多い．そして，学生にその違いを強要する人も少なくないらしい．しかし，上記のようにこの発音の違いはどうでもいい問題だと思う．心配なら，it の母音の「エ」とも「イ」ともつかないあの母音でいつも発音しておけば完全に間違いない．「ザ」と「ジ」というどうせ間違っている区別を教えるよりもずっといい．