First, we define Trigonometry as one of the branches of Mathematics that studies relationships that involves lengths and angles of triangles while Physics is the natural science that involves the study of matter and its motion through space and time, along with related topics such as force and energy. So, what's really their relationship as an application to each other.
-----Actually, Trigonometry is used to many different topics related to Physics and what are those? In Trigonometry, we solve angles and lengths that is use too in Physics, we do solve anything that involves a vector such as forces, electric fields, magnetic fields and others.