Rewrite \(\displaystyle{f{{\left({x}\right)}}}={3}{\sin{{\left(\pi{x}\right)}}}+{3}\sqrt{{{3}}}+{3}\sqrt{{{3}}}{\cos{{\left(\pi{x}\right)}}}\) in the form \(\displaystyle{f{{\left({x}\right)}}}={A}{\sin{{\left({K}{x}+{D}\right)}}}\)

palmantkf4u

palmantkf4u

Answered question

2022-03-31

Rewrite f(x)=3sin(πx)+33+33cos(πx) in the form f(x)=Asin(Kx+D)

Answer & Explanation

Brennan Thompson

Brennan Thompson

Beginner2022-04-01Added 10 answers

This is a standard thing:
3sin(πx)+23cos(πx)=(3)2+(33)2
=6(36sin(πx)+336cos(πx))
=6(12sin(πx)+32cos(πx))
=6(cosαsin(πx)+sinαcos(πx))
=6(cosαsin(πx)+sinαcos(πx))
=6sin(πx)+α)
I leave it to you to figure out what number α is.

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