TrigFcns - 6-masala yechimi | MathModel.uz

1.3-bo'lim : Trig funktsiyalari

6. Kalkulyatordan foydalanmasdan $\displaystyle \sec \left( { - \frac{{11\pi }}{6}} \right)$ ning aniq qiymatini aniqlang.

Yechim

Birinchidan, biz $\frac{\pi }{6} - 2\pi = - \frac{{11\pi }}{6}$ va shunga o'xshash (manfiy burchaklar soat yo'nalishi bo'yicha aylantirilishini esga olib) biz $ - \frac{{11\pi }}{6}$ uchun terminal chizig'i birinchi kvadrantda musbat $x$ o'qi bilan $\frac{\pi }{6}$ burchagini hosil qilishini ko'rishimiz mumkin. Boshqacha qilib aytganda, $ - \frac{{11\pi }}{6}$ va $\frac{\pi }{6}$ bir xil burchakni ifodalaydi. Shunday qilib, biz ushbu muammo uchun quyidagi birlik doirasiga ega bo'lamiz.

$A unit circle with the angles $\frac{\pi }{6}$, $\frac{\pi }{4}$ and $\frac{\pi }{3}$ drawn in the first quadrant and labeled with the coordinates $\left( {\frac{{\sqrt 3 }}{2},\frac{1}{2}} \right)$, $\left( {\frac{{\sqrt 2 }}{2},\frac{{\sqrt 2 }}{2}} \right)$ and $\left( {\frac{1}{2},\frac{{\sqrt 3 }}{2}} \right)$ where they meet the circle. The axes are labeled with the angles 0 and $2\pi $, $\frac{\pi }{2}$, $\pi $ and $\frac{{3\pi }}{2}$ and the points (1,0), (0,1), (-1,0) and (0,-1). The line for the angle $\frac{\pi }{6}$ is also labeled $ - \frac{{11\pi }}{6}$, showing that the two angles end on the same line.$

2-qadam

Ikki burchak $ - \frac{{11\pi }}{6}$ va $\frac{\pi }{6}$ bir xil koordinatalarga ega bo'lgani uchun javob:

\[\sec \left( -\frac{11\pi }{6} \right)=\frac{1}{\cos \left( -\frac{11\pi }{6} \right)}=\frac{1}{{}^{\sqrt{3}}/{}_{2}}=\frac{2}{\sqrt{3}}\]