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    In Q9iia) why is the least value 1/12 and not -1/4. I obtained the 1/12 so I know that it is derived from setting cos(theta) to equal 1. But setting cos(theta) to equal -1 gives the value -1/4. So why is the the incorrect solution?
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    It's something along the lines of, raising cosx or sinx to any power above 1 will have a max value of 1 and a min of 0

    I.e cos^a(x) can be between 1 and 0, where a is number greater than 1.

    Google a graphing calculator and sketch it out yourself. You'll see cos^2(x) will have a max of 1 and min of 0

    With that in mind, can you see how, the question you've given will give a greatest value of 1/4 and smallest of 1/12?
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    The fraction is \frac{1}{8cos^4\theta +4}, due to the power 4, the denominator will always be positive. For the smallest value of a fraction the denominator has to be as large as possible, as 1 divided by a large number is a small number, now consider what value of cos(\theta) makes the denominator as large as possible.
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    (Original post by NotNotBatman)
    The fraction is \frac{1}{8cos^4\theta +4}, due to the power 4, the denominator will always be positive. For the smallest value of a fraction the denominator has to be as large as possible, as 1 divided by a large number is a small number, now consider what value of cos(\theta) makes the denominator as large as possible.
    This is a much better explanation than mine lol I can't talk math online
 
 
 
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