Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary.
-$$f ( x ) = 4 \sin 3 x - 2 \cos 3 x$$
A) $\mathrm { a } = 6.00 , \mathrm {~b} = 2 , \mathrm {~h} = 0.63$
B) $\mathrm { a } = 4.47 , \mathrm {~b} = 6 , \mathrm {~h} = 0.15$
C) $\mathrm { a } = 0.15 , \mathrm {~b} = 3 , \mathrm {~h} = 4.47$
D) $\mathrm { a } = 4.47 , \mathrm {~b} = 3 , \mathrm {~h} = 0.15$

Question

Quizplus · Accepted Answer

To express $f(x) = 4 \sin 3x - 2 \cos 3x$ in the form $a \sin(b(x - h))$, we use the identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$. Comparing coefficients, we find $a = \sqrt{4^2 + (-2)^2} = 4.47$, $b = 3$, and $h = \arctan\left(\frac{-2}{4}\right)/3 = 0.15$ (in radians).

Find A, B, and H So That F(x) a Sin f(x)=4sin⁡3x−2cos⁡3xf ( x ) = 4 \sin 3 x - 2 \cos 3 xf(x)=4sin3x−2cos3x

Find A, B, and H So That F(x) a Sin $f ( x ) = 4 \sin 3 x - 2 \cos 3 x$