The same as it is now : measurement of angles and the lengths of the sides of triangular shapes. More complex shapes ha to be broken down into triangles.
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It is certainly used in calculus, just as calculus can be used in trigonometry.
Trigonometry is used to find the distance and angle of atoms that are bonding. Oh this is for chemistry by the way hope this was helpful. :)
Yes.
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Optics deals with light waves, and all waves relate in some way to trigonometry. Also, the reflection and refraction of light involves trigonometry.