164. ա) sin2α — cos2α + 1 / sin2α = sin2α — cos2α + sin2α + cos2α / sin2α = 2sin2α/sin2α = 2

բ) cos4α — sin4α / sin2α — cos2α = (cos2α — sin2α)(cos2α + sin2α) / sin2α — cos2α = cos2α — sin2α / sin2α — cos2α = -(cos2α — sin2α) / cos2α — sin2α = -1

գ) (cosα — sinα)2 — 2sinαcosα = cos2α +2sinαcosα + sin2α — 2sinαcosα = cos2α + sin2α = 1

դ) sin4α — cos4α + 2sin2αcos2α = (sin2α + cos2α)2 = 1^2 = 1

165. ա) 1/tg2α + 1/ctg2α = 1 / 1/cos2α + 1 / 1/sin2α = cos2α + sin2α = 1

բ) 1/tgα + 1/ctgα — 1/sinαcosα = ctgα + tgα — 1/sinαcosα = cosα/sinα + sinα/cosα — 1/sinαcosα = cos2α + sin2α — 1 / sinαcosα = 0

166. ա) (sinβ — cosβ)2 + (sinβ + cosβ)2 = 2

sin2β — 2sinβcosβ + cos2β + sin2β + 2sinβcosβ + cos2β = 2(sin2β + cos2β) = 2

բ) (tgα + ctgα)2 — (tgα — ctgα)2 = 4

(tgα + ctgα)2 — (tgα — ctgα)2 = tg2α + 2tgαctgα + ctg2α — tg2α + 2tgαctgα — ctg2α = 4tgαctgα = 4

գ) tg2x — 1 / tg2x + 1 +cos2x = sin2x

tg2x — 1 / tg2x + 1 + cos2x = tg2x — 1 + cos2x * (sin2x/cos2x + 1) / tg2x + 1 = tg2x — 1 + sin2x + cos2x / tg2x + 1 = tg2x/tg2x + 1 = sin2x / cos2x * 1/cos2x = sin2x

Vox Pops World Famous Report / answer the questions in written form./

Which three factors do you think are important to have a good quality of life?

I think firstly environment, the people around you make a strong inpact on the person. If the family and friends are good, supportive, funny, kind and undertsanding, the person will be too, so the quality of his life becomes better.
Secondly I would say is health, because health is the key to living longer and having no trouble in the future.
And the last I would say financial status, because nowdays money is really important for affording good healthcare and everything you need for a good quality of life.

Navigate Reading slide82 ex 6
Watch the video Happiness in Mexico, slide 85, ex 4/ be ready to discuss in class

6. Read an online aticle about culture shock. What four different stages can you identify? What stage do you think Julia is at?

The first stage is filled with positive thoughts, when the person is excited and facsinated by the new people, language and culture.
The second stage is filled with frustration, when the person is misunderstood by the new environment, people make fun of you for being a bit different.
The third stage is about adjustment to the new environment, the person’s sense of humor is back and he starts to enkoy time there more.
And the final fourth stage is about fully adapting and becoming happier.

4. Watch again. Decide if sentences a-f are true (T), false (F) or if the video doesn’t say (DS). Correct the false sentences.

a. health and wealth are two most important factors when measuring a population’s happiness. T
b. Denmark was higher on the list than all the other northern European countries. T
c. most people expected Mexico to be higher on the list than the USA. F
In Mexico, …
d. people know that their families will usually help them when life gets difficult. T
e. it is normal for people to meet up with their neighbours. T
f. the fine weather is the main reason for the population’s happiness. T

Ռազմական հետախուզությունը լինում է երեք տեսակի՝ ռազմավարական, մարտավարական, օպերատիվ: Ինչպես նաև ռազմական հետախուզությունը ունի իր յոթ հիմնական վարման ձևերը.

1. Դիտարկում
2. Գաղտնալսում
3. Որոնում
4. Դարանակալում
5. Հետախուզություն մարտով
6. Հանկարծակի հարձակում
7. Գերիների և տեղաբնակների հարցաքննում

504 Essential Words Sharp words make more wounds than surgeons can heal.” in some sentences comment on the quote

We all know that there is a phisical pain and a mental one. While you can heal a physical wound, it’s really hard to heal a mental wound. Many people don’t think before saying something, sometimes they think that they are just honest with the person, but there is a border between honesty and insult. So the bad words someday can really hurt somebody, especially if the person is insecure. They can’t forget it for a long time, constantly repeating it in their mind. People should learn to be more tactful.

Words to learn slide 41 ignite, abolish, urban…. , slide 43 Fill in the Blanks, Word Detective

Fill in the Blanks
Place one of the new words in each of the blanks below.

1. The doctor was completely frank with the dying man.
2. In an audible whisper, Maria called for my attention.
3. We didn’t need any evidence to see that the poor man was in urgent need of money and food.
4. All his life the child was used to living in urban areas.
5. Dry matches to ignite the campfire were sought by the boy scout.
6. Smoking is prohibited in the medical building.
7. Gasoline fumes help to pollute the air.
8. The decrease in the number of people voting in national elections is due to lack of interest.
9. Some citizens believe that we will never be able to abolish war.
10. The population of New York City is about eight million people.
11. In the comics, Superman never reveals his true identity.
12. They needed an abequate supply of water to last for the entire trip through the desert.

Word Detective
From the list of 12 new words that follows, choose the one that corresponds to each definition below.

1. Having to do with cities or towns — urban
2. make known — reveal
3. as much as is needed; sufficient — adequate
4. make dirty — pollute
5. do away with completely — abolish
6. make or become less — decrease
7. free in expressing one’s thoughts — frank
8. demanding immediate action — urgent
9. set on fire — ignite
10. people of a city or country — population
11. able to be heard — audable
12. forbid by law or authority — prohibit

162. ա) sinα — sin³α / cosα — cos³α = sinα (1 — sin²α) / cosα (1 — cos²α) = sinα * cos²α / cosα * sin²α = cosα/sinα = ctgα

բ) sin³α — sin⁵α / cos³α — cos⁵α = sin3α (1 — sin2α) / cos3α (1 — cos2α) = sin3α * cos2α / cos3α — sin2α = sinα / cosα = tgα

գ) tgα ctgα — cos2α / sinα = tgα * 1/tgα -cos2α / sinα = 1 — cos2α / sinα = sin2α / sinα = sinα

դ) 1 — cos2α / 1 — sin2α + tgα ctgα = sin2α / cos2α + tgα * 1/tgα = sin2α/cos2α + 1/1 = sin2α/cos2α + cos2α/cos2α = sin2α + cos2α / cos2α = 1/cos2α

504 Essential Words slide 38, / words to learn/ slide 39 Fill in the Blanks, Matching

Fill in the Blanks
Place one of the new words in each of the blanks below.

1. The old man had lived for seven decades.
2. He had the vision that some day there would be peace on earth.
3. Only a minority of the senators were against welfare.
4. No one has ever had even a glimpse of the future.
5. People used to think it was an absurd idea that human beings could ever fly.
6. We make frequent visits to Florida in the winter.
7. If you have any questions, don’t hesitate to ask.
8. There was only a solitary man on the beach.
9. The conflict was over the highcost of bread.
10. Recent studies have shown that the cost of living has gone up rapidly.
11. The gun alone was evidence enough to convict the killer.
12. The stories Henry told people about his adventures turned out to be merely fiction.

Matching
Match the 12 new words in Column I with the definitions in Column II.

1. vision — h. sense of sight
2. fiction — g. that which is imagined or made up
3. frequent — b. happening often
4. absurd — plainly not true or sensible
5. minority — i. smaller number or part
6. evidence — d. that which makes clear the truth or falsehood of something
7. conflict — j. direct opposition
8. decade — a. ten years
9. glimpse — f. a short, quick view
10. recent — e. occurring not long ago
11. solitary — c. alone
12. hesitate — fail to act quickly

Naviaget Watch the video Moving abroad to work In some sentences write about the video. slide 75
Navigate Review slide 76 1a,2a 3a

Shujana is from Szeged, a small town in Hungary. Like many others, she moved to another country to find a job. Now, she has been living in Oxford for over 4 years. She used to teach English and German in Hungary, but then she decided she needed a change, so she moved to England. Currently, she tests digital products for software.
There are many differences between Hungary and England. Things are more expensive in England than in Hungary. In Hungary, it’s hard to find a good job, so many people move abroad, mostly to Germany, Austria and UK. After a few years, they often want to go back home because of their families and friends.

1a. Read the sentences and cross out the forms which are not possible. Sometimes both forms may be correct.

1. When I was little, I used to want to be a pop star when I grew up.
2. I would practise in front of the mirror with a hairbrush as a microphone.
3. My mother would laugh, but kindly.
4. She would/used to tell me that I could be anything I wanted.
5. But she would/used to warn me that it wouldn’t be easy to be a pop star.
6. I really used to believe I could do it, but now I’m quite happy being a dentist!

2a. Make questions using the prompts.

1. What does being succesful mean to you?
2. Who is succesful in your family?
3. What is your biggest goal in life?
4. What is one job you wouldn’t like to do?
5. Which is better — an indoor or outdoor job? Why?
6. What is your dream job?

3a. Read the text and complete it with one word in each space. The first letter is given.

1 — working hours, 2 — salary, 3 — working conditions, 4 — promotion, 5 — career prospects, 6 — redundant