Tìm tổng tất cả các nghiệm của phương trình

Tìm tổng các nghiệm của phương trình $\sin (5x + \frac{\pi }{3}) = \cos (2x - \frac{\pi }{3})$ trên ${\rm{[}}0;\pi {\rm{]}}$ A. $\frac{{7\pi }}{{18}}$ B. $\frac{{4\pi }}{{18}}$ C. $\frac{{47\pi }}{8}$ D. $\frac{{47\pi }}{{18}}$

Phương trình $ \Leftrightarrow \sin (5x + \frac{\pi }{3}) = \sin (\frac{{5\pi }}{6} - 2x)$ $ \Leftrightarrow \left[ \begin{array}{l}5x + \frac{\pi }{3} = \frac{{5\pi }}{6} - 2x + k2\pi \\5x + \frac{\pi }{3} = \frac{\pi }{6} + 2x + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{14}} + k\frac{{2\pi }}{7}\\x = - \frac{\pi }{{18}} + k\frac{{2\pi }}{3}\end{array} \right.$. $ \bullet $ Với $x = \frac{\pi }{{14}} + k\frac{{2\pi }}{7} \Rightarrow 0 \le \frac{\pi }{{14}} + k\frac{{2\pi }}{7} \le \pi $ $ \Leftrightarrow - \frac{\pi }{{14}} \le k\frac{{2\pi }}{7} \le \frac{{13\pi }}{{14}} \Leftrightarrow - \frac{1}{4} \le k \le \frac{{13}}{4}$. Do $k \in \mathbb{Z} \Rightarrow k \in \left\{ {0,1,2,3} \right\}$ Suy ra các nghiệm: $x = \frac{\pi }{{14}},x = \frac{{5\pi }}{{14}},x = \frac{{9\pi }}{{14}},x = \frac{{13\pi }}{{14}}$ $ \bullet $ Với $x = - \frac{\pi }{{18}} + k\frac{{2\pi }}{3} \Rightarrow 0 \le - \frac{\pi }{{18}} + k\frac{{2\pi }}{3} \le \pi $ $ \Leftrightarrow \frac{\pi }{{18}} \le k\frac{{2\pi }}{3} \le \frac{{19\pi }}{{18}} \Leftrightarrow \frac{1}{{12}} \le k \le \frac{{19}}{{12}}$. Do $k \in \mathbb{Z} \Rightarrow k = 1$ Suy ra các nghiêm: $x = \frac{{11\pi }}{{18}}$.

Vậy tổng các nghiệm là: $\frac{{47\pi }}{{18}}$.

Tìm tổng các nghiệm của phương trình trên .

A.

A.

B.

B.

C.

C.

D.

D.

Đáp án và lời giải

Đáp án:D

Lời giải:

Đáp án là D

Phương trình

. Với . Do Suy ra các nghiệm: Với . Do Suy ra các nghiêm: . Vậy tổng các nghiệm là: .

Đáp án đúng là D

Câu hỏi thuộc đề thi sau. Bạn có muốn thi thử?

Bài tập trắc nghiệm 45 phút Bài toán về phương trình lượng giác cơ bản, nâng cao - Toán Học 11 - Đề số 9

Làm bài

Chia sẻ

Một số câu hỏi khác cùng bài thi.

• Giải phương trình

  
  .

• Mệnh đề nào dưới đây đúng?

• Cho phương trình

  
  . Tính tổng các nghiệm của phương trình trong khoảng
  

• Nghiệm của pt

  
  .

• Cótấtcảbaonhiêugiátrịnguyêncủathamsố

  
  đểphươngtrình
  
  cónghiệm?

• Tìm tổng các nghiệm của phương trình

  trên
  .

• Phương trình

  
  tương đương với phương trình:

• Nghiệm của phương trình

  
  là:

• Số giá trị nguyên của tham số

  
  thuộc đoạn
  
  để phương trình
  

• Tìm m để phương trình

  
  có nghiệm
  
  .

• Nghiệm của phương trình

  
  thỏa điều kiện:
  
  .

• Trên khoảng

  
  , phương trình
  
  :

• Nghiệm của phương trình

  
  là:

• Giảiphươngtrình

  
  .

• Phương trình

  
  có một họ nghiệm là:

• Sốvịtríđiểmbiểudiễncácnghiệmcủaphươngtrình

  
  trênđườngtrònlượnggiáclà:

• Phương trình

  
  :

• Nghiệm của phương trình

  
  thỏa điều kiện
  
  .

• Phương trình

  
  có bao nhiêu nghiệm thuộc khoảng
  
  ?

• Biết các nghiệm của phương trình

  
  có dạng
  
  và
  
  ,
  
  ; với
  
  là các số nguyên dương. Khi đó
  
  bằng

• Phươngtrình

  
  tươngđươngvớiphươngtrình.

• Có bao nhiêu số nguyên

  
  để phương trình
  
  có nghiệm?

• Phương trình:

  
  có các nghiệm là:

• Tính tổng

  
  các nghiệm của phương trình
  
  trên khoảng
  

• Phương trình nào trong số các phương trình sau có nghiệm?

Một số câu hỏi khác có thể bạn quan tâm.

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 32 to 36:

  School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

  Question 35:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 31 to 35:

  Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can helpa person understand these changes and provide him(35)____the skills for adjusting to them.

  Question 31:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 32 to 36:

  School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

  Question 34:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 31 to 35:

  Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can helpa person understand these changes and provide him(35)____the skills for adjusting to them.

  Question 34:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 31 to 35:

  Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can helpa person understand these changes and provide him(35)____the skills for adjusting to them.

  Question 33:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

  Few people now realize the reality of global warming and its effects on the world’s climate. Many scientists (24) _______ the blame for recent natural disasters on the increase in the world’s temperatures and are convincedthat, more than ever before, the Earth is at (25) _______ from the forces of the wind, rain and sun. According tothem, global warming is making extreme weather events, such as hurricanes and droughts, even more severe andcausing sea levels all around the world to rise. Environmental groups are putting pressure on governments to take action to reduce the amount of carbondioxide which is given (26) _______ by factories and power plants, thus attacking the problem at its source. They are in (27) _______ of more money being spent on research into solar, wind, and wave energy devices, which could then replace existing power (28) _______. Some scientists, however, believe that even if we stoppedreleasing carbon dioxide and other gases into the atmosphere tomorrow, we would have to wait several hundred years to notice the results. Global warming, it seems, is to stay.

  Question 25:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

  Few people now realize the reality of global warming and its effects on the world’s climate. Many scientists (24) _______ the blame for recent natural disasters on the increase in the world’s temperatures and are convincedthat, more than ever before, the Earth is at (25) _______ from the forces of the wind, rain and sun. According tothem, global warming is making extreme weather events, such as hurricanes and droughts, even more severe andcausing sea levels all around the world to rise. Environmental groups are putting pressure on governments to take action to reduce the amount of carbondioxide which is given (26) _______ by factories and power plants, thus attacking the problem at its source. They are in (27) _______ of more money being spent on research into solar, wind, and wave energy devices, which could then replace existing power (28) _______. Some scientists, however, believe that even if we stoppedreleasing carbon dioxide and other gases into the atmosphere tomorrow, we would have to wait several hundred years to notice the results. Global warming, it seems, is to stay.

  Question 24:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

  On a winter afternoon, a dozen male Northernfur seals are on an island off south - westernAlaska. To look at them, fighting for territoryon the rocks, it’s hard to imagine that they areat the (27)____________of a bafflingscientific mystery: why is this species beginning to disappear?These seals - which can weigh up to 270kilograms - have an important and symbolic(28)_________in Alaska’s history. Their softand luxurious fur, the coveted prize duringthe huge commercial sea harvests that werelegal here in the Bering Sea through the early 20th century, was once so valuable it(29)_________Alaska’s economy. Starting in the 1950s, for reasons that are(30)_______because the harvests by thentended to be fairly small, the seal populationbegan a slow decline. But lately it has beenfalling drastically, declining at an alarming(31)________of 6 per cent a year since 1998.From a (32)_________ of more than 2million in Alaska in 1948, their numbers havefallen to about 1 million. So (33)________, no one has been able toestablish a precise cause for this, although theories (34)___________. The seal's foodsupply may be (35)________, or anotherspecies may be (36)________on the seals -perhaps killer whales, which no longer haveas many great whales to eat because ofharvesting of those mammals. Some peoplehave suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alonecould (38)_________the recent population decline.

  Question 35:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

  On a winter afternoon, a dozen male Northernfur seals are on an island off south - westernAlaska. To look at them, fighting for territoryon the rocks, it’s hard to imagine that they areat the (27)____________of a bafflingscientific mystery: why is this species beginning to disappear?These seals - which can weigh up to 270kilograms - have an important and symbolic(28)_________in Alaska’s history. Their softand luxurious fur, the coveted prize duringthe huge commercial sea harvests that werelegal here in the Bering Sea through the early 20th century, was once so valuable it(29)_________Alaska’s economy. Starting in the 1950s, for reasons that are(30)_______because the harvests by thentended to be fairly small, the seal populationbegan a slow decline. But lately it has beenfalling drastically, declining at an alarming(31)________of 6 per cent a year since 1998.From a (32)_________ of more than 2million in Alaska in 1948, their numbers havefallen to about 1 million. So (33)________, no one has been able toestablish a precise cause for this, although theories (34)___________. The seal's foodsupply may be (35)________, or anotherspecies may be (36)________on the seals -perhaps killer whales, which no longer haveas many great whales to eat because ofharvesting of those mammals. Some peoplehave suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alonecould (38)_________the recent population decline.

  Question 34:

• Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

  On a winter afternoon, a dozen male Northernfur seals are on an island off south - westernAlaska. To look at them, fighting for territoryon the rocks, it’s hard to imagine that they areat the (27)____________of a bafflingscientific mystery: why is this species beginning to disappear?These seals - which can weigh up to 270kilograms - have an important and symbolic(28)_________in Alaska’s history. Their softand luxurious fur, the coveted prize duringthe huge commercial sea harvests that werelegal here in the Bering Sea through the early 20th century, was once so valuable it(29)_________Alaska’s economy. Starting in the 1950s, for reasons that are(30)_______because the harvests by thentended to be fairly small, the seal populationbegan a slow decline. But lately it has beenfalling drastically, declining at an alarming(31)________of 6 per cent a year since 1998.From a (32)_________ of more than 2million in Alaska in 1948, their numbers havefallen to about 1 million. So (33)________, no one has been able toestablish a precise cause for this, although theories (34)___________. The seal's foodsupply may be (35)________, or anotherspecies may be (36)________on the seals -perhaps killer whales, which no longer haveas many great whales to eat because ofharvesting of those mammals. Some peoplehave suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alonecould (38)_________the recent population decline.

  Question 31: