Question

Am I dealing with harmonic stuff (trig)?

Answer 1

You just need to solve for when
`y=0`:

`\frac{\cos8t-9\sin8t}4=0\implies\cos8t-9\sin8t=0`

`\implies\cos8t=9\sin8t`

`\implies\frac19=(\sin8t)/(\cos8t)=\tan8t`

`\implies8t=\tan^(-1)\frac19+n\pi`

`\implies t=\frac18\tan^(-1)\frac19+\frac{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=\frac18\tan^(-1)\frac19\approx0.01`

`t=\frac18\tan^(-1)\frac19+\frac\pi8\approx0.41`

`t=\frac18\tan^(-1)\frac19+\frac\pi4\approx0.80`