 Kendall Holder

2022-01-23

P(t) models the distance of a swinging pendulum (In CM) from the place it has travelled t seconds after it starts to swing. Here, t is entered in radians.
$P\left(t\right)=-5\mathrm{cos}\left(2\pi t\right)+5$
What is the first time the pendulum reaches 3.5 CM from the place it was released?
Ok, so I did this to get the solution:
$3.5=-5\mathrm{cos}\left(2\pi t\right)+5$
$-1.5=-5\mathrm{cos}\left(2\pi t\right)$
$0.3=\mathrm{cos}\left(2\pi t\right)$
$\mathrm{cos}-1\left(0.3\right)=2\pi t$
$\frac{{\mathrm{cos}}^{-1}\left(0.3\right)}{2\pi }=t$
The fact is this gives me 11.55 seconds to get to 3.5 CM, which does not sound right. Where did I go wrong and how can I fix it? Fallbasisz8

Expert

Obviously you're expecting the input to cos in radians because you have . In physics you always use radians.
However, you can get it to work in degrees with a slight modification: change $2\pi$ to 360. Don't make it a habit though. Stay away from degrees.

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