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Trigonometry is used to define triangles, but it is also useful in the representation of waves. Sound engineers, obviously, use deal with sound waves. The pitch, volume, and direction of a sound wave are all deeply rooted in trigonometry.
Engineers and Physicists use trigonometry, as well as people whose carrers involve acoustics, optics, and waves.
how can trigonometry use in metallurgy
That depends on your profession. If you are a math teacher, then you might use a lot of Trig. If you are an engineer, working with forces on any object from different directions, then you would use trig. Electrical engineers use trig. Surveyors use trig.
One example of an astronomer's use of trigonometry is determining the distance to a star by triangulation.