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Find the range of possible values of sin(x)^3 - sin(x)^2, where x is a real number.

 Jun 17, 2020
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The absolute value of sin3(x) is always going to be less than or equal to that of sin2(x), so the difference will be negative or zero.  The minimum will occur when sin(x) = -1, so the range will be -2 <= sin3(x) -  sin2(x) <= 0.

 Jun 17, 2020
edited by Alan  Jun 17, 2020

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