Question

Помогите решить последние 5)Пожалуйста)

Answer 1

10.

$2 \cos{5t} < \sqrt{2} \ ;$

$\cos{5t} < \frac{ \sqrt{2} }{2} \ ;$

$5t \in ( \ \frac{ \pi }{4} + 2 \pi n \ ; \ \frac{7}{4} \pi + 2 \pi n \ ) \ , \ n \in Z \ ;$

$t \in ( \ \frac{ \pi }{20} + \frac{ 2 \pi n }{5} \ ; \ \frac{7}{20} \pi + \frac{ 2 \pi n }{5} \ ) \ , \ n \in Z \ ;$


11.

$-\frac{ \sqrt{3} }{2} \leq \cos{t} < -\frac{1}{2} \ ;$

$t \in [ \ -\frac{5}{6} \pi + 2 \pi n \ ; \ -\frac{2}{3} \pi + 2 \pi n \ ) \cup ( \ \frac{2}{3} \pi + 2 \pi n \ ; \ \frac{5}{6} \pi + 2 \pi n \ ] \ , \ n \in Z \ ;$



12.

$| \cos{t} | \geq \frac{ \sqrt{2} }{2} \ ;$

$t \in [ \ -\frac{ \pi }{4} + \pi n \ ; \ \frac{ \pi }{4} + \pi n \ ] \ , \ n \in Z \ ;$



13.

$| tg{(t)} | > 2 \ ;$

$| \frac{1}{ Ctg{(t)} } | > 2 \ ;$

$\frac{1}{ | Ctg{(t)} | } > 2 \ ;$

$| Ctg{(t)} | < \frac{1}{2} \ ;$

$t \in ( \ arcCtg{ \frac{1}{2} } + \pi n \ ; \ arcCtg{ ( -\frac{1}{2} ) } + \pi n \ ) \ , \ n \in Z \ ;$



14.

$3 \sin{ ( 2t - \frac{ \pi }{4} ) } \leq 1 \ ;$

$\sin{ ( 2t - \frac{ \pi }{4} ) } \leq \frac{1}{3} \ ;$

$\cos{ ( \frac{ \pi }{2} - [ 2t - \frac{ \pi }{4} ] ) } \leq \frac{1}{3} \ ;$

$\cos{ ( [ 2t - \frac{ \pi }{4} ] - \frac{ \pi }{2} ) } \leq \frac{1}{3} \ ;$

$-\cos{ ( [ 2t - \frac{ \pi }{4} ] + \frac{ \pi }{2} ) } \leq \frac{1}{3} \ ;$

$-\cos{ ( 2t + \frac{ \pi }{4} ) } \leq \frac{1}{3} \ ;$

$\cos{ ( 2t + \frac{ \pi }{4} ) } \geq -\frac{1}{3} \ ;$

$( 2t + \frac{ \pi }{4} ) \ \in \ \ [ \ \ -arccos{ ( -\frac{1}{3} ) } + 2 \pi n \ \ ; \ \ arccos{ ( -\frac{1}{3} ) } + 2 \pi n \ \ ] \ , \ n \in Z \ ;$

$2t \ \in \ \ [ \ \ -arccos{ ( -\frac{1}{3} ) } - \frac{ \pi }{4} + 2 \pi n \ \ ; \ \ arccos{ ( -\frac{1}{3} ) } - \frac{ \pi }{4} + 2 \pi n \ \ ] \ , \ n \in Z \ ;$

$t \ \in \ \ [ \ \ -\frac{1}{2} arccos{ ( -\frac{1}{3} ) } - \frac{ \pi }{8} + \pi n \ \ ; \ \ \frac{1}{2} arccos{ ( -\frac{1}{3} ) } - \frac{ \pi }{8} + \pi n \ \ ] \ , \ n \in Z \ .$