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The obvious answer is to impart a sound knowledge of the subject in the students. However, you probably want to know why anyone wants to learn trigonometry. The answer to that is this.

Trigonometry is a mathematical tool which is almost essential to know if you want to understand how to build structures cheaply and effectively. With trig. it's easy to figure out where things are most likely to break and how thick structural parts must be to carry loads safely. Trig. is also very useful to understand waves - all sorts of waves such as radio waves and waves on water.

Without trig. engineers would waste so much time trying to work things out that they'd never succeed in any job.

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Q: What are the objectives of teaching trignometry?
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