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The equation is 
the -30 expression, is subtracting, if negative, from the 60
if the cosine returned is negative, you'd end up with a +30,
negative * negative = positive
and then the 30 expression will ADD to the 60 amount
so the temperature "t" is highest, when the 30 expression, is
positive and and it's highest
when does that happen, when cosine is negative and at its highest,
well, cosine range is
so the lowest value cosine can provide is -1, when is cosine -1?
well, at
so... let's find a value that makes that expression to
![\bf t=60-30 cos (x \frac{\pi}{6}) \qquad x=6 \\\\ thus \\\\ t=60-30 cos (6 \frac{\pi}{6})\implies t=60-30 cos (\pi ) \\\\ t=60-30[-1]\implies t=60+30\implies t=90](https://tex.z-dn.net/?f=%5Cbf%20t%3D60-30%20cos%20%28x%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%5Cqquad%20x%3D6%0A%5C%5C%5C%5C%0Athus%0A%5C%5C%5C%5C%0At%3D60-30%20cos%20%286%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%5Cimplies%20t%3D60-30%20cos%20%28%5Cpi%20%29%0A%5C%5C%5C%5C%0At%3D60-30%5B-1%5D%5Cimplies%20t%3D60%2B30%5Cimplies%20t%3D90)
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so...for August, that'll mean
the -30 expression, is subtracting, if negative, from the 60
if the cosine returned is negative, you'd end up with a +30,
negative * negative = positive
and then the 30 expression will ADD to the 60 amount
so the temperature "t" is highest, when the 30 expression, is
positive and and it's highest
when does that happen, when cosine is negative and at its highest,
well, cosine range is
so the lowest value cosine can provide is -1, when is cosine -1?
well, at
so... let's find a value that makes that expression to
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so...for August, that'll mean