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alekssr [168]
4 years ago
11

Am I dealing with harmonic stuff (trig)?

Mathematics
1 answer:
pochemuha4 years ago
8 0

You just need to solve for when y=0:

\dfrac{\cos8t-9\sin8t}4=0\implies\cos8t-9\sin8t=0

\implies\cos8t=9\sin8t

\implies\dfrac19=\dfrac{\sin8t}{\cos8t}=\tan8t

\implies8t=\tan^{-1}\dfrac19+n\pi

\implies t=\dfrac18\tan^{-1}\dfrac19+\dfrac{n\pi}8

where n is any integer. We only care about when 0\le t\le1, which happens for n\in\{0,1,2\}.

t=\dfrac18\tan^{-1}\dfrac19\approx0.01

t=\dfrac18\tan^{-1}\dfrac19+\dfrac\pi8\approx0.41

t=\dfrac18\tan^{-1}\dfrac19+\dfrac\pi4\approx0.80

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