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can someone explain why to find fbx you use sine instead of cosine?

why was the substitution necessary
I don't understand that part

Are you referring to the substitution at 3:25? "Substitution" is a strategy for solving sets of related equations (technically called "simultaneous" equations. These are equations that all contain the same variables for the same physical situation). Substitution replaces an unknown variable with an expression containing a different variable, and this process goes on until we're left with an equation containing only one variable, which we can then solve for. Chapter 4 of https://openstax.org/details/books/intermediate-algebra might be helpful.