No. Trigonometry will have little effect on being able to win at billiards or pocket billiards. A study of physics will do more, but only the simplest bank shots are aided by these sciences. The stroke and alignment are more important, and the knowlege of the more complex factors in the game than trigonometry is needed for complex shots.
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No. Trigonometry alone will not make you able to win at billiards, even though trigonometry is involved in calculating angles. For the same reason, physics alone won't do it. The primary ability to win at billiards is skill.