Hi, there!
I’ve experienced “office love” when working at a trading company.
She was working for the import section, being sweet and lovely.
Somewhere between one and two years, we were just exchanging
social pleasantries.
However, I started to feel an irresistible desire to meet personally
with her immediately after my manager had assigned me to go on
a three-month business trip to Latin America. I couldn’t see what
would happen on the upcoming trip, being apprehensive about
whether I could make my missions possible.
One day, I called her from a phone booth, almost at midnight, and
she seemingly managed to stammer in speechless amazement.
――”Where are you?” asked she.
Suddenly an ambulance sped along the street in front of me. My
doe-eyed co-worker didn’t fail to hear the sound on the receiver.
――”You idiot!?” assailed my ears.
The receiver seemed to drop off the table.
It is an undisputed authentic story. I am faithful to a woman. I’ve
never ever been in a love triangle before, I swear. Please access
my Kindle Unlimited site here if you want to read more.
Today, let me challenge a word problem related to the trigonome-
tric ratio. I’ll be watchful not to be in a triangle relation.
The number of solutions \(x\) to the equation \(7\sqrt{3}sin\,x + 2cos^{2}x\)
\(= 11\), in the range \(0\leq x <2π\), is ( ).
(Source: Question similar to The University of Oxford,
Maths Admissions Test)
\(7\sqrt{3}sin\,x + 2cos^{2}x = 11\)
Using the identify \(sin^{2}x + cos^{2}x = 1\), I see
\(7\sqrt{3}sin\,x + 2cos^{2}x = 11\)
\(7\sqrt{3}sin\,x + 2(1 – sin^{2}x) = 11\)
\(2sin^{2}x – 7\sqrt{3}sin\,x + 9 = 0\)
\((2sin\,x – \sqrt{3})(sin\,x – 3\sqrt{3}) = 0\)
Now \(sin\,x = 3\sqrt{3}\) has no solutions, and in the range \(0\leq x < 2π\),
I note \(sin\,x\) takes the value \(\frac{\sqrt{3}}{2}\) twice at \(\frac{π}{3}\) and at \(\frac{2}{3}π\).
Therefore, the answer is 2.
Bear in mind,
\(\frac{π}{3} = \frac{180°}{3} = 60° (sin60°)\), and
\(\frac{2}{3}π = \frac{360°}{3} = 120° (sin120°)\)
Now I’ve mellowed out since I weathered a lot of hardships.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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