Sin(3pi/2 - 2x) = sin x; x∈ [ 3pi/2; 5 pi/2]. - cos 2x = sin x ; - (1 - 2 sin^2 x) - sin x = 0; 2 sin^2 x - sin x - 1= 0; sin x = t; - 1 ≤ t ≤ 1; 2t^2 - t - 1 = 0; t1 = 1 ; ⇒ sin x = 1; x = pi/2 + 2pik; t2 = - 1/2; ⇒sin x = - 1/2; x = (-1)^(k+1)*pi/6 + pi*k.
1 yesterday i had breakfast at the canteen. 2 last summer we went to the black sea. 3 he didn't call me last week. 4 why did this girl come to our office yesterday? 5 when did you buy tickets last time? 6 last june the boys played football every morning. 7 on sunday my parents were at the theatre. 8 i didn't take part at the conference last month. 9 he lived in kiev in his childhood. 10 where did he send his message? 2 трансформируйте предложения в past simplе 1 he often played chess. 2 our classes began at 9 a. m. 3 she was always busy. 4 what did you do in the evening? 5 my sister didn’t study at school, she worked at the hospital. 6 my friend prefered tea to coffee. 7 i found many stories in this magazine. 8 he was in my room, wasn't he? 9 why did you always ask so many questions? 10 jasmine seldom visited her grandparents. 3 образуйте отрицательную форму предложений 1 in summer she didn't get up early. 2 mr. white didn't write a lot of letters yesterday. 3 on friday they weren't at the station. 4 we didn't enjoy our time in rome. 5 they didn't watch a football match last weekend. 6 the girl didn't open a box at once. 7 i didn't leave my keys on the table. 8 the engineer didn't go on business trip on monday. 9 my friend didn't want to move to another flat. 10 i didn't find a surprise in the present-box. 4 поставьте вопросы к предложениям. 1 he learned english at school. (where? what language? why? or …? ) where did he learn english? what language did he learn? why did he learn english? did he learn english or french? 2 the train was five hours late. (what? why? ) what was 5 hours late? why was the train five hours late? 3 i was going to stay at my aunt’s in the crimea. (where? who? or …? ) where was i going to stay in the crimea? who was going to stay at the aunt's in the crimea? was i going to stay at my aunt's or in the hotel in the crimea? 4 they stayed in moscow only for two days. (why? where? how long? ) why did they stay in m only for 2 days? where did they stay? how long did they stay in m? 5 i bought a very beautiful dress in this shop last weekend. (where? what? when? ) where did i buy a very beautiful dress last weekend? what did i buy in this shop last weekend? when did i buy this beautiful dress in the shop? 6 they traveled to cyprus by sea. (how? where? or …? ) how did they travel to c? where did they travel to? did they travel to c or ibiza? 7 i didn’t find your telephone number. (what? why? ) what didn't i find? why didn't i find your telephone number? 8 in his childhood he was always a leader among his friends. (what? when? who? ) what was he in his childhood? when was he a leader among his friends? who was always a leader among his friends in his childhood? 9 he caught a cold last month. (what? when? why? ) what did he catch? when did he catch a cold? why did he catch a cold? 10 we did our lessons together. (what? how? ) what did we do together? how did we do our lessons?
x∈ [ 3pi/2; 5 pi/2].
- cos 2x = sin x ;
- (1 - 2 sin^2 x) - sin x = 0;
2 sin^2 x - sin x - 1= 0;
sin x = t; - 1 ≤ t ≤ 1;
2t^2 - t - 1 = 0;
t1 = 1 ; ⇒ sin x = 1; x = pi/2 + 2pik;
t2 = - 1/2; ⇒sin x = - 1/2; x = (-1)^(k+1)*pi/6 + pi*k.
[3pi/2; 5pi/2].
x = 11pi/6; x = 5pi/2