TrigFcns - 10-masala yechimi | MathModel.uz

1.3-bo'lim : Trig funktsiyalari

10. Kalkulyatordan foydalanmasdan $\displaystyle \sin \left( { - \frac{{11\pi }}{3}} \right)$ ning aniq qiymatini aniqlang.

Yechim

Avval biz $\frac{\pi }{3} - 4\pi = - \frac{{11\pi }}{3}$ ekanligini va $4\pi $ ikkita to'liq aylanish ekanligini ta'kidlaymiz (shuningdek, manfiy burchaklar soat yo'nalishi bo'yicha aylantirilishini yodda tutsak) biz $ - \frac{{11\pi }}{3}$ va $\frac{\pi }{3}$ uchun terminal chizig'i bir xil burchak ekanligini ko'rishimiz mumkin va shuning uchun 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 $\frac{\pi }{3}$ is also labeled $ - \frac{{11\pi }}{3}$, showing that the two angles end on the same line.$

2-qadam

$ - \frac{{11\pi }}{3}$ va $\frac{\pi }{3}$ bir xil burchak bo'lgani uchun javob:

\[\sin \left( { - \frac{{11\pi }}{3}} \right) = \frac{{\sqrt 3 }}{2}\]