Phương trình \(\sin x = \frac{2}{3}\) có số nghiệm trong khoảng \(\left( { - \pi ;\pi } \right)\) là:
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có: \(\sin x = \frac{2}{3} \Leftrightarrow \left[ \begin{array}{l}x = \arcsin \frac{2}{3} + k2\pi \\x = \pi - \arcsin \frac{2}{3} + k2\pi \end{array} \right.\,\,\left( {k \in Z} \right)\)
\(\begin{array}{l}
- \pi < \arcsin \frac{2}{3} + k2\pi < \pi \mathop \Leftrightarrow \limits^{k \in Z} \frac{{ - \pi - \arcsin \frac{2}{3}}}{{2\pi }} < k < \frac{{\pi - \arcsin \frac{2}{3}}}{{2\pi }}\mathop \Leftrightarrow \limits^{k \in Z} - 0,61 < k < 0,38 \Leftrightarrow k = 0\\
\Rightarrow x = \arcsin \frac{2}{3} = \arcsin \frac{2}{3}.\\
- \pi < \pi - \arcsin \frac{2}{3} + k2\pi < \pi \mathop \Leftrightarrow \limits^{k \in Z} \frac{{ - 2\pi + \arcsin \frac{2}{3}}}{{2\pi }} < k < \frac{{\arcsin \frac{2}{3}}}{{2\pi }}\mathop \Leftrightarrow \limits^{k \in Z} - 0,88 < k < 0,12\mathop \Leftrightarrow \limits^{k \in Z} k = 0.\\
\Rightarrow x = \pi - \arcsin \frac{2}{3} = \pi - \arcsin \frac{2}{3}.
\end{array}\)
Vậy có 2 nghiệm thỏa mãn yêu cầu bài toán.
Chọn C.
Bộ Đề Kiểm Tra Giữa Học Kì I - Toán 11 - Các Trường THPT Trên Toàn Quốc không chỉ giúp học sinh củng cố kiến thức đã học mà còn rèn luyện khả năng tư duy logic và giải quyết vấn đề nhanh chóng, chính xác. Đề thi bao gồm các dạng bài tập đa dạng để các em chuẩn bị tốt cho kỳ thi khác.
Câu hỏi liên quan
Cách thời điểm này đúng một năm, Quỹ Phát triển KH&CN Quốc gia (NAFOSTED) tổ chức lễ kỷ niệm 20 năm thành lập với niềm vui của một tổ chức đã làm thay đổi diện mạo của nền khoa học Việt Nam xen lẫn nỗi ngơ ngác chứng kiến sự chuyển đổi cơ chế quản lý tài chính. Sự đan xen của hai sắc thái này càng được tô đậm khi nguyên Bộ trưởng Bộ KH&CN Hoàng Văn Phong, trong lễ kỷ niệm vào tháng 12/2023, đã nhận xét “Mọi người ai cũng nói, hoạt động của NAFOSTED cũng giống hoạt động của các tổ chức quốc tế nhưng thật ra mà nói, trong bối cảnh Việt Nam, quỹ vừa hoạt động như tổ chức tài chính nhà nước, vừa là đơn vị sự nghiệp”.
Chính hai cái áo cùng khoác lên NAFOSTED đã tạo ra sự linh hoạt trong các hoạt động tài trợ, hỗ trợ của quỹ trong suốt thời gian tồn tại. “Là đơn vị tài chính của ngành khoa học, NAFOSTED được giao quản lý, điều hành một khoản vốn điều lệ và khoản tiền này được mặc nhiên định vào trong kế hoạch. Do đó, Quỹ không phải dự toán để xây dựng kế hoạch mà là triển khai kế hoạch theo kinh phí đã được bố trí”, nguyên Bộ trưởng Hoàng Văn Phong nói. Nằm dưới sự quản lý của Bộ KH&CN và không chạy theo các hoạt động tài trợ để thu lợi nhuận như các quỹ tài chính thông thường, NAFOSTED đương nhiên là một đơn vị sự nghiệp – lợi nhuận của NAFOSTED, nếu coi là như vậy, là những “khoản lãi” sẽ đến trong tương lai thông qua việc gia tăng tiềm lực KH&CN và nguồn nhân lực chất lượng cao cho đất nước.
Suốt hai thập niên, NAFOSTED vẫn là một mô hình tài trợ cho khoa học duy nhất ở khu vực công theo cơ chế quỹ, một cơ chế mà theo TS. Nguyễn Quân, nguyên Bộ trưởng Bộ KH&CN “nói nôm na là tiền chờ đề tài chứ không phải đề tài chờ tiền”. Tuy nhiên, vị thế này giờ đã được “hóa giải” bằng Luật Ngân sách 2015, đưa NAFOSTED trở lại quỹ trong ngân sách với quỹ đạo tài chính truyền thống giống các chương trình KH&CN khác.
Đó là lý do mà bên lề lễ kỷ niệm, một nhà vật lý từng giành giải thưởng Tạ Quang Bửu nhận xét “Tính thông thoáng và linh hoạt vốn có của cơ chế quỹ có thể sẽ không còn” trong khi một nhà quản lý kỳ cựu dự báo, “NAFOSTED sẽ rất khó khăn nếu không bảo vệ được cơ chế quỹ”.
Những dự báo này, theo thời gian, đã trở thành thực tế không thể chối bỏ. Vậy cách nào để tháo gỡ, nếu không muốn mai một đi một mô hình đã đem lại sức sống mới cho khoa học Việt Nam?
(Theo Thanh Nhàn, NAFOSTED: Bao giờ trở lại ngày xưa?)
Tại sao các nhà khoa học và quản lý lo ngại về sự thay đổi cơ chế của NAFOSTED?
Số tập hợp con của tập hợp A có 5 phần tử là :
Có tất cả mấy bước lập kế hoạch tài chính cá nhân?
Rửa xe, đánh bóng vỏ xe là công việc bảo dưỡng cơ bản nào?
Mục đích tham gia hợp tác xã của các thành viên là gì?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Who are you?
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MacMaster's invention is an example of sock puppetry: the use of false identities to deceive others. (I). The false identity is known as a sock puppet, and its creator, a puppet master. (II). MacMaster created Amina to express his views on Middle Eastern affairs without offending other Americans. (III). Writing as Amina gave him the authority to say what he wanted. (IV).
At the turn of the millennium, Debbie Swenson created Kaycee Nicole, a fictional teenage girl suffering from terminal cancer. Her blog, Living Colours, described Kaycee’s struggle, attracting millions of readers. When Kaycee 'died' on 14 May 2001, her fans were devastated. Their distress turned to anger when they discovered that Kaycee was not real. Swenson had developed the character to gain attention and sympathy.
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Yet none of these stories compare to large-scale sock puppetry today. The New York City Police Department has false identities on social media to catch criminals. The US military is believed to use sock puppets to track potential terrorists. It is clear that the internet is a minefield today and we all have to step very carefully in order not to get hurt.
According to the passage, which of the following statements is TRUE?
Tổng số hạt proton, neutron và electron có trong nguyên tử là
Nội dung nào sau đây là yếu tố quyết định để khẳng định: Đảng Cộng sản Việt Nam ra đời (1930) đã chấm dứt thời kì khủng hoảng về đường lối cứu nước ở Việt Nam?
Read the following passage about the Science in Service of Humanity and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Science has come out of its shell in laboratories to become a powerful force for human advancement. Modern scientific endeavors increasingly focus on addressing real-world challenges affecting communities globally. From developing vaccines that save millions to creating technologies connecting people across continents, science serves humanity in countless ways. This shift represents a fundamental evolution in how we perceive scientific progress—not merely academic pursuit but a practical tool for improving lives and solving pressing problems.
[I] Medical breakthroughs exemplify how science directly benefits humanity. [II] For instance, gene therapy offers hope for those with inherited conditions, while artificial intelligence helps diagnose diseases earlier and more accurately. [III] These advancements didn't happen overnight; scientists had to burn the midnight oil for years before achieving success. [IV] Their perseverance demonstrates that when science targets humanitarian goals, results can transform society profoundly.
Environmental science has emerged as another crucial domain where laboratory work translates into human welfare. Climate scientists provide data informing policy decisions affecting billions. Conservation biologists develop strategies to protect biodiversity, ensuring future generations benefit from natural resources. Agricultural researchers create drought-resistant crops helping communities withstand changing climate conditions. Despite these contributions, environmental science faces challenges including funding limitations, political resistance, and urgency of addressing accelerating climate change. Nevertheless, dedicated scientists continue their work, recognizing environmental health directly impacts human wellbeing.
The future of science in service of humanity looks increasingly collaborative and inclusive. Modern approaches incorporate diverse perspectives, including indigenous knowledge and community participation. Citizen science projects engage non-professionals in data collection, democratizing the scientific process. Open-access publishing makes research findings available to anyone with internet access, not just wealthy institutions. These developments suggest science's greatest potential lies in becoming more accessible and responsive to human needs. As we face complex global challenges, from pandemics to climate change, science serving humanity offers our best hope for a sustainable future.
Which of the following is TRUE according to the passage?
Hình thức hoạt động của Việt Nam Quang phục hội trong thời gian chiến tranh thế giới thứ nhất là
Read the following passage about Wildlife Conservation in Africa and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Wildlife conservation in Africa is vital for preserving biodiversity and ensuring the survival of iconic species such as elephants, lions, and rhinos. [I] The continent is home to some of the world’s most diverse ecosystems, including savannahs, rainforests, and deserts. [II] Conservation efforts involve strategies like protecting habitats, combating poaching, and raising awareness about the importance of wildlife. [III] Despite challenges, success stories demonstrate the positive impact of these efforts. [IV]
One notable example comes from Kenya, where anti-poaching initiatives and community engagement have helped stabilize elephant populations in Amboseli National Park. Similarly, in South Africa, rhino conservation programs use advanced technologies like drones and GPS tracking to monitor and protect vulnerable animals. These efforts not only safeguard wildlife but also promote eco-tourism, which supports local economies.
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Which of the following best paraphrases the underlined sentence in paragraph 4?
"Initiatives like eco-tourism provide financial incentives for communities to protect wildlife.”
Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions
[I] A newborn baby can see, hear and feel. By the age of five, a child can talk, ride a bike and invent imaginary friends. How does this development happen? [II]We don't understand the way language, thinking and planning develop very well. [III]Now scientists are using new technology to ‘see’ into children's brains. And they are discovering new information about the way a baby's brain develops. [IV]
A study in 2010 showed that children who were afforded more focus often gained an edge in IQ. The brain of a newborn infant contains nearly a hundred billion neurons. This number is comparable to that of an adult's brain. As they mature, an infant assimilates information through the sensory modalities of sight, hearing, smell, taste, and touch. This information fosters intricate connections between different regions of the brain. By the age of three, there are approximately a hundred trillion synaptic connections.
One experiment looked at images of babies' brains while they were listening to different sounds. The sounds were in different sequences. For example, one sequence was mu-ba-ba. This is the pattern ‘A-B-B’. Another sequence was mu-ba-ge. This is the pattern ‘A-B-C’. The images showed that the part of the brain responsible for speech was more active during ‘A-B-B’ patterns. This shows that babies can tell the difference between different patterns. This experiment is interesting because sequences of words are important to grammar and meaning. Compare two sentences with the same words in a different order: ‘John killed the bear’ is very different from ‘The bear killed John.’ So babies are starting to learn grammatical rules from the beginning of life.
Researchers also know that babies need to hear a lot of language in order to understand grammar rules. But there is a big difference between listening to television, audiobooks or the internet, and interacting with people. One study compared two groups of nine-month-old American babies. One group watched videos of Mandarin Chinese sounds. In the other group, people spoke the same sounds to the babies. The test results showed that the second group could recognize different sounds, however, the first group learned nothing. The scientist, Patricia Kuhl, said this result was very surprising. It suggests that social experience is essential to successful brain development in babies.
According to paragraph 3, which of the following is NOT a finding of the sound sequence experiment?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions from 41 to 45.
When parents name their children, they often take into consideration their own preferences, family traditions, or beliefs. In many European cultures, parents typically select names based on family connections, often honoring grandparents or ancestors. For instance, in Italy, children are commonly named after their grandparents, starting with the father's parents and then the mother's. Similarly, in Eastern Europe, children may be named after their deceased relatives to protect them from harm.
In some Asian countries, the naming process may involve the child's grandfather or a fortune-teller, who chooses a name believed to shape the child's character. Names might be inspired by elements like fire, water, earth, wood, or metal, or they may convey qualities such as beauty, strength, or kindness.
African cultures also have unique naming traditions, such as in Ghana's Akan culture, where a child's name is determined by the day of their birth. Each day has specific names for boys and girls, reflecting characteristics associated with that day. For example, a boy born on Friday might be named Kofi, symbolizing a "wanderer" or "explorer" while a girl born on the same day could be named Afua, also representing a traveler.
No matter where a name originates, it holds significant meaning and reflects the child's cultural heritage. Whether chosen out of preference or dictated by tradition, a child's name is a cherished and respected gift.
It can be inferred from the passage that names in China would relate to______.
Nội dung nào dưới đây không phải nhược điểm của cơ chế thị trường?
Quốc gia nào phát triển mạnh năng lượng tái tạo?
Cho HS \(f(x) = \left\{ \begin{array}{l}\sqrt {x + 1} - 2\quad (x \ge - 1)\\3{x^2} - x + 1\quad (x < - 1)\end{array} \right.\). Tính giá trị của \(2.f( - 3) - 4.f(0)\)?
Đâu là nội dung thể hiện trách nhiệm của công dân trong việc tham gia vào các hoạt động kinh tế?
Nền kinh tế nước ta có mấy hình thức sở hữu?
CHỦ ĐỀ: TẠI SAO CON NGƯỜI KHÔNG BỊ KHÍ QUYỂN ĐÈ ÉP?
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 21)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d0afa01ca011
Và trả lời câu hỏi sau:
Xác định nội dung chính của bài viết.
Read the following passage about food addiction and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Few people would disagree that one of the world's most popular dishes is pizza. Twenty-two-year-old Zack certainly wouldn't. He would eat a variety of pizza-based items, including homemade pizza, precooked microwave pizza, and even pizza leftovers from the night before. He was consuming 800kg of pizza a year. As a child, Zack had eaten a wide variety of food. But he became addicted to pizza when he started secondary school. American school meals have often been criticised for the large amount of fast food present on the menu, and pizza is the star dish. Zack even spent all his pocket money on slices of pizza.
Naturally, Zack's family worried about his high-calorie, low-vitamin diet. So did Zack. In an attempt to break his addiction, Zack agreed to appear on a TV programme called Freaky Eaters. Its aim was to encourage food addicts to beat their addictions with the help of a psychologist and nutritionist. It wasn't easy. He had to eat a fish dish, while his brother sat in front of him enjoying... a pizza! However, Zack met the challenge and has never eaten pizza again.
Seventeen-year-old Stacy Irvine's friends visit her and discover that she has been rewarded thousands of free toys from fast food restaurants as a regular customer. Stacy's mother often gave her two-year-old girl a portion of fried chicken in a McDonald's restaurant. [I] Since then, Stacy has refused to eat anything else except for pieces of fried chicken, and as a result, her diet has created serious health. She has been warned that if she doesn't change her diet, she will die. [II] Stacy once collapsed due to lack of vitamins and nutrients and needed to be hospitalised. [III] She insisted that Stacy adopt a healthier lifestyle. However, worryingly, Stacy's mother said that while Stacy was beginning to understand the seriousness of her situation, she couldn't eat anything else but chicken nuggets. [IV]
Twenty-year-old Hanna Little was keen on chips. The only thing that Hanna consumed for fifteen years was one plate of chips after another. Not surprisingly, a diet that contained few nutrients and an excess of fat and carbohydrates could only have negative consequences. And it did because not only did Hanna develop health problems, but she also had to leave her job after collapsing at work. At five, Hanna became addicted to chips and refused to eat fruits and vegetables despite her mother's efforts. Hanna says that she was terrified of tasting the flavour of different types of food and she would feel anxious just at the idea of doing it. Parties, picnics and barbecues with friends and family used to be a nightmare. Furthermore, Hanna was soon seen as 'odd' by her friends' parents.
It wasn't until the age of sixteen that Hanna realised she had Selective Eating Disorder (SED). Despite this new knowledge, no solution was found. It wasn't until she lost her job before she started eating normally. Hanna sought therapy from psychologist Felix Economakis, who used hypnosis, a treatment that none of the doctors that she had seen before had mentioned, to get her to eat fruit after one one-hour session, and since then she has been willing to eat anything.... including chips!
(Adapted from Friends Global)
The word it in paragraph 4 refers to _____.
