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I am trying to solve the following inequality equation in Mathematica:

12 Sin[300 t] >= 8

I want to find the values of t that satisfy this inequality. I have tried using the Solve and Reduce functions, but I haven't been successful so far. Here's the code I've used:

Solve[12 Sin[300 t] >= 8, t]

and

Reduce[12 Sin[300 t] >= 8, t]

Unfortunately, both attempts didn't work. Could someone please guide me on how to correctly solve this inequality equation in Mathematica?

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    $\begingroup$ Try Reduce[12 Sin[300 t] >= 8, t, Reals] $\endgroup$
    – Moo
    May 17, 2023 at 12:02

1 Answer 1

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Just simplifying to look at one cycle:

res = Reduce[Sin[300 t] >= 2/3 && 0 < t < Pi/150, t]

yields: 1/300 ArcSin[2/3] <= t <= 1/300 ([Pi] - ArcSin[2/3])

Visualing:

pts = {res[[1]], res[[-1]]};
Plot[Sin[300 t], {t, 0, Pi/150}, Frame -> True, 
 GridLines -> {pts, {2/3}}, 
 Epilog -> {Red, Arrowheads[{-.03, .03}], Arrow[{#, 0} & /@ pts]}]

enter image description here

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