Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary.
-$$f ( x ) = 5 \cos x + 2 \sin x$$
A) $a = 7.00 , b = 2 , h = - 0.79$
B) $a = 1.19 , b = 1 , h = 5.39$
C) $a = 5.39 , b = 1 , h = - 1.19$
D) $a = 5.39 , b = 2 , h = 1.19$

Question

Quizplus · Accepted Answer

To convert $f(x) = 5\cos(x) + 2\sin(x)$ to the form $a\sin(b(x - h))$, we use the identity $\sin(x) = \cos(\frac{\pi}{2} - x)$ and the sum-to-product formulas. The given function can be rewritten using a common angle formula, resulting in $a = \sqrt{5^2 + 2^2} = 5.39$, $b = 1$, and $h = -\arctan(\frac{2}{5}) = -1.19$.

Find A, B, and H So That F(x) a Sin f(x)=5cos⁡x+2sin⁡xf ( x ) = 5 \cos x + 2 \sin xf(x)=5cosx+2sinx

Find A, B, and H So That F(x) a Sin $f ( x ) = 5 \cos x + 2 \sin x$