Solving \(\displaystyle{a}{\sin{\theta}}+{b}{\cos{\theta}}={c}\) I know that the solution is

Alfredo Holmes

Alfredo Holmes

Answered question

2022-04-01

Solving asinθ+bcosθ=c
I know that the solution is
θ=tan1ca2+b2c2+tan1ab

Answer & Explanation

arrebusnaavbz

arrebusnaavbz

Beginner2022-04-02Added 18 answers

here is a trick: write
aa2+b2sin(θ)+ba2+b2cos(θ)=ca2+b2
Setting
cos(ϕ)=aa2+b2
and
sin(ϕ)=ba2+b2
then you will get
sin(ϕ+θ)=ca2+b2
so
θ=arcsin(ca2+b2)ϕ

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