Answer: True
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Step-by-step explanation:
The function can be broken down into the form
f(x) = g(x) - 3*h(x)
where,
g(x) = sin(x)
h(x) = cos(x)
Both g and h are sinusoidal with the same period of 2pi. Therefore, the linear combination of these functions is also sinusoidal with the same period of 2pi. If the periods didn't match up, then it's likely the function isn't sinusoidal and instead some other complicated crazy curve.
Extra notes:
- A sinusoidal curve is one that has a steady up and down smooth sine curve to it. Think of a simple ocean wave.
- A cosine curve is really a sine curve in disguise. It's been phase shifted 90 degrees or pi/2 radians. It's not a coincidence that the word "sine" is found in "cosine".
- When I say "period of 2pi", I mean the curve repeats itself every 2pi radians. This is equivalent to 360 degrees. The repeating pattern goes on forever.