Determine whether the graph of f(x) is a sinusoid.
-$$f ( x ) = \sin 7 \pi x - \cos 4 \pi x$$

Question

Quizplus · Accepted Answer

A sinusoid is a function that can be written in the form $A \sin(Bx - C) + D$ or $A \cos(Bx - C) + D$, where $A$, $B$, $C$, and $D$ are constants. The given function $f(x) = \sin 7 \pi x - \cos 4 \pi x$ is a combination of a sine and a cosine function with different frequencies, and it cannot be rewritten as a single sine or cosine function due to the differing frequencies (7π and 4π). Therefore, it is not a sinusoid.

Determine Whether the Graph of F(x) Is a Sinusoid f(x)=sin⁡7πx−cos⁡4πxf ( x ) = \sin 7 \pi x - \cos 4 \pi xf(x)=sin7πx−cos4πx

Determine Whether the Graph of F(x) Is a Sinusoid $f ( x ) = \sin 7 \pi x - \cos 4 \pi x$