Asosiy tarkibga o'tish

1.10-bo'lim : Umumiy grafiklar

Grafik kalkulyatordan foydalanmasdan \(h\left( x \right) = \cos \left( {x + \frac{\pi }{2}} \right)\) grafigini chizing.

Yechim

Asosiy algebraik o'zgarishlarni eslang. Agar biz \(g\left( x \right)\) grafigini bilsak, \(g\left( {x + c} \right)\) grafigi oddiygina \(g\left( x \right)\) ning grafigi, agar \(c < 0\) bo'lsa, \(c\) birliklari bilan o'ngga siljigan yoki \(c > 0\) bo'lsa, \(c\) birliklari bilan chapga siljigan.

Shunday qilib, bizning holatlarimizda \(g\left( x \right) = \cos \left( x \right)\), biz buni ko'rishimiz mumkin,

\[h\left( x \right) = \cos \left( {x + \frac{\pi }{2}} \right) = g\left( {x + \frac{\pi }{2}} \right)\]

va shuning uchun bizdan eskiz qilishimiz so'ralgan grafik \(\frac{\pi }{2}\) birliklari tomonidan chapga siljitilgan kosinus funksiyasining grafigi.

Mana \(h\left( x \right) = \cos \left( {x + \frac{\pi }{2}} \right)\) grafigi va shuni yodda tutingki, transformatsiyani ko'rishga yordam berish uchun biz \(g\left( x \right) = \cos \left( x \right)\) grafigida ham chizganmiz.

The graph of \(h\left( x \right) = \cos \left( {x + \frac{\pi }{2}} \right)\), drawn as a solid red curve, along with the graph of \(g\left( x \right) = \cos \left( x \right)\), drawn as a dashed gray curve, for \( - 2\pi \le x \le 2\pi \).  Both curves oscillate between -1 and 1.  Arrows point to a peak on each curve.  The graph of \(g\left( x \right)\) has a peak at \(x = 0\) and the graph of \(h\left( x \right)\) has a peak at \(x = - \frac{\pi }{2}\), so the graph of \(h\left( x \right)\) is the graph of \(g\left( x \right)\) shifted left \(\frac{\pi }{2}\) units.