The word trigonometry is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 20
Highest Scoring Words With Friends™ Play In The Letters trigonometry
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Seven Letter Word Alert: (24 words)
emoting, emotion, ergonym, gritter, groomer, ionomer, mitogen, mongery, monitor, mooring, mooting, omitter, orogeny, regroom, retying, roomier, rooming, rooting, rotting, tooting, torment, tornote, torrent, trionym