Question

f(x) =3sin(2x) + 2cos(2x)

Answer 1

\[=√(2^2+3^2)cos(2x- \phi); \phi = arctan(3/2)\]\[=√13cos(2x-\phi)\]

Answer 2

what is arctan(3/2)?

Answer 3

\[0.983...\]OR
\[56.31°\]

Answer 4

so the best answer is just
\[=√13cos(2x−arctan(3/2))\]

Answer 5

Is that
\[=\sqrt{13\cos(2x−\arctan(3/2))}\]where the whole thing is rooted?

Answer 6

no, only the 13 is in the square root
\[=\sqrt(13) cos(2x−arctan(3/2))\]

Answer 7

Yes that is correct, but it is not neat, here is a more neat answer
\[=√(13)\sin(2x+\arctan(2/3))\]

Answer 8

that is much better thankyou