In the previous problem, the function $x$ can be written as
A) $x = 3 \sin ( t + \phi ) , \text { where } \tan \phi = - 4 / 3$
B) $x = 4 \sin ( t + \phi ) , \text { where } \tan \phi = - 4 / 3$
C) $x = 5 \sin ( t + \phi ) , \text { where } \tan \phi = - 4 / 3$
D) $x = 5 \sin ( t + \phi ) , \text { where } \tan \phi = - 3 / 4$
E) $x = 4 \sin ( t + \phi ) , \text { where } \tan \phi = - 3 / 4$

Question

Quizplus · Accepted Answer

The correct choice is C because the function $x$ can be represented in the form of $x = A \sin(t + \phi)$, where $A$ is the amplitude and $\phi$ is the phase shift. The amplitude is given by the square root of the sum of the squares of the coefficients in front of the sine and cosine (if the original function was a combination of these), which often comes from the Pythagorean identity. Given $\tan \phi = -4/3$, it suggests a right triangle in the coordinate system where the opposite side is 4 units and the adjacent side is -3 units, leading to a hypotenuse (and thus the amplitude) of 5, following the Pythagorean theorem. Therefore, the correct representation is with an amplitude of 5 and a phase shift where $\tan \phi = -4/3$.

In the Previous Problem, the Function xxx Can Be Written as A)

In the Previous Problem, the Function $x$ Can Be Written as
A)