Sine and Cosine Inequality Problems

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.

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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

To solve this algebraically, we set can set up the following equation

h ≥ 1.5

h = sin(t) + 1

By substitution we can get the equation of the inequality that we actually want to solve 1.5 ≥ sin(t) + 1

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