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Sine and Cosine Inequality Problems

How to solve inequalities

theorem here
If you are trying to solve sine and cosine inequality problems, then you should already understand how the graph below represents the equation of
y = sin(x) +1.
Graph of regular sine
By changing a few words, we can rework the problem above into a real world problem (soon enough it will be an inequalty problem, don't worry!). The graph below represents the height of a roller coaster over time.(Yes I know that it's not a very high roller coaster, given that it maxes out at 2 ...but let's pretend that this is the graph of Thomas the Tank Engine roller coaster.)

An actual Inequality Problem



Here's the inequality problem based on the graph above. During what interval of time is the train at least 1.5 above the ground?
Answer
Another roller coaster is modelled by the euqation h =cos(t) +2 . During what interval of time from 0≤ t ≤ 2Π . Is the roller coaster at least at a height of 2?
Answer

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