Project ID:
7100020188
Accepted:
Typ:
Layout:
Question:
Priraďte ku každej goniometrickej nerovnici jej množinu riešení.
Question 1:
$\sin x > \frac12$
Answer 1:
$$
\bigcup_{k \in \mathbb{Z}} \left( \frac{\pi}{6} + 2k\pi ,\frac{5\pi}{6} + 2k\pi \right)
$$
Question 2:
$$
\mathrm{tg}\, x > 1
$$
Answer 2:
$$
\bigcup_{k \in \mathbb{Z}} \left( \frac{\pi}{4} + k\pi ,\frac{\pi}{2} + k\pi \right)
$$
Question 3:
$\mathrm{cotg}\, x < -1$
Answer 3:
$$
\bigcup_{k \in \mathbb{Z}} \left( \frac{3\pi}{4} + k\pi , \pi + k\pi \right)
$$
Question 4:
$\sin x < -\frac{\sqrt2}2$
Answer 4:
$$
\bigcup_{k \in \mathbb{Z}} \left( \frac{5\pi}{4} + 2k\pi ,\frac{7\pi}{4} + 2k\pi \right)
$$
Question 5:
$\mathrm{tg}\, x < \sqrt3$
Answer 5:
$$
\bigcup_{k \in \mathbb{Z}} \left( -\frac{\pi}{2} + k\pi ,\frac{\pi}{3} + k\pi \right)
$$
Question 6:
$\mathrm{cotg}\, x > 0$
Answer 6:
$$
\bigcup_{k \in \mathbb{Z}} \left( 0+ k\pi ,\frac{\pi}{2} + k\pi \right)
$$
Question 7:
$\sin x <- \frac12$
Answer 7:
$$
\bigcup_{k \in \mathbb{Z}} \left( \frac{7\pi}{6} + 2k\pi ,\frac{11\pi}{6} + 2k\pi \right)
$$
Question 8:
$\cos x > \frac{\sqrt3}2$
Answer 8:
$$
\bigcup_{k \in \mathbb{Z}} \left( -\frac{\pi}{6} + 2k\pi ,\frac{\pi}{6} + 2k\pi \right)
$$
Question 9:
$\sin x < \frac{\sqrt3}2$
Answer 9:
$$
\bigcup_{k \in \mathbb{Z}} \left( -\frac{4\pi}{3} + 2k\pi ,\frac{\pi}{3} + 2k\pi \right)
$$