1.5-bo'lim : Trig tenglamalarni kalkulyator yordamida yechish, I qism
12. \(\left[ { - 4,6} \right]\) da joylashgan \(\displaystyle \frac{4}{3} = 1 + 3\sec \left( {2t} \right)\) yechimini toping. Ishingizda kamida 4 kasrdan foydalaning.
Yechim
Tenglamaning bir tomonida sekantni (bir koeffitsient bilan) izolyatsiya qilish,
\[\sec \left( {2t} \right) = \frac{1}{9}\]Shu nuqtada biz to'xtashimiz mumkin. Biz buni bilamiz
\[\sec \theta \le - 1\hspace{0.25in}\,\,\,\,\,{\rm{or}}\hspace{0.25in}\,\,\,\,\sec \theta \ge 1\]Bu shuni anglatadiki, sekant hech qachon \(\frac{1}{9}\) bo'lishi mumkin emas va shunday bo'ladi yechim yo'q bu tenglamaga.
E'tibor bering, agar siz sekantdagi limitlarni eslamagan bo'lsangiz, keyingi qadam buni kosinusga aylantirish bo'lar edi, shuning uchun buni qilaylik.
\[\sec \left( {2t} \right) = \frac{1}{{\cos \left( {2t} \right)}} = \frac{1}{9}\hspace{0.50in} \Rightarrow \hspace{0.50in}\cos \left( {2t} \right) = 9\]Shu nuqtada shuni ta'kidlashimiz mumkinki, \( - 1 \le \cos \theta \le 1\) va shunga o'xshash yana kosinusning 9 bo'lishining iloji yo'q va yana biz borligini tushunamiz. yechim yo'q bu tenglamaga.