اختبار حل معادلات المثلثات مع الحلول العامة

Question 1

حل على $[0,2\pi)$: $\sin x=\frac{\sqrt{3}}{2}$.

Accepted Answer

$x=\frac{\pi}{3},\ \frac{2\pi}{3}$

Answer

$x=\frac{\pi}{3}$

Answer

$x=\frac{\pi}{6},\ \frac{5\pi}{6}$

Answer

$x=\frac{2\pi}{3},\ \frac{5\pi}{3}$

Question 2

حل على $[0,2\pi)$: $	an x\,(\sec x-1)=0$.

Accepted Answer

$x=0,\ \pi$

Answer

$x=0$

Answer

$x=\frac{\pi}{2},\ \frac{3\pi}{2}$

Answer

$x=0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$

Question 3

حل لجميع قيم $x$ الحقيقية: $\sin(2x)+\sin x=0$.

Accepted Answer

$x=k\pi$ or $x=\frac{2\pi}{3}+2k\pi$ or $x=\frac{4\pi}{3}+2k\pi$

Answer

$x=k\pi$

Answer

$x=\frac{\pi}{3}+2k\pi$ or $x=\frac{5\pi}{3}+2k\pi$

Answer

$x=\frac{2\pi}{3}+2k\pi$

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