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    Sine and Cosine Inequality Problems

    How to solve inequalities

    Sine and cosine inequality problems take several forms. This page will explore an inequality created by a line and a cosine or sine graph.
    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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