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以下为一些大学高数中三角函数图象相关的题目及答案示例： **一、图象变换类题目** 1. **题目** - 将函数\(y = \sin(\frac{\pi}{2}x+\frac{\pi}{4})\)的图象上各点的纵坐标不变，横坐标伸长到原来的2倍，再向右平移\(\frac{\pi}{4}\)个单位，求所得到的图象解析式。 2. **答案** - 首先，对于函数\(y = \sin(\frac{\pi}{2}x+\frac{\pi}{4})\)，横坐标伸长到原来的2倍（即\(x\)的系数变为原来的\(\frac{1}{2}\)），得到\(y=\sin(\frac{\pi}{4}x+\frac{\pi}{4})\)。 - 然后再向右平移\(\frac{\pi}{4}\)个单位，根据“左加右减”原则，\(x\)变为\(x-\frac{\pi}{4}\)，得到\(y = \sin[\frac{\pi}{4}(x - \frac{\pi}{4})+\frac{\pi}{4}]=\sin(\frac{\pi}{4}x-\frac{\pi^{2}}{16}+\frac{\pi}{4})=\sin(\frac{\pi}{4}x+\frac{(4 - \pi)\pi}{16})\)。 **二、根据图象求函数表达式类题目** 1. **题目** - 已知三角函数图象的最大值是\(\frac{3}{2}\)，从\(-\frac{\pi}{6}\)到\(\frac{5\pi}{6}\)是一个周期，图象为\(y = A\sin(\omega x+\varphi)\)（\(A>0,\omega>0\)且\(|\varphi|<\frac{\pi}{2}\)）的形式，求函数表达式。 2. **答案** - 因为最大值是\(\frac{3}{2}\)，所以\(A=\frac{3}{2}\)。 - 周期\(T=\frac{5\pi}{6}-(-\frac{\pi}{6})=\pi\)，又因为\(T=\frac{2\pi}{\omega}\)且\(\omega>0\)，所以\(\omega = 2\)，此时函数为\(y=\frac{3}{2}\sin(2x+\varphi)\)。 - 当\(x = -\frac{\pi}{6}\)时，\(y = 0\)，即\(\frac{3}{2}\sin(-\frac{\pi}{3}+\varphi)=0\)，也就是\(\sin(-\frac{\pi}{3}+\varphi)=0\)，\(-\frac{\pi}{3}+\varphi = k\pi\)（\(k\in Z\)），\(\varphi=k\pi+\frac{\pi}{3}\)。 - 由于\(|\varphi|<\frac{\pi}{2}\)，当\(k = 0\)时，\(\varphi=\frac{\pi}{3}\)，所以函数表达式为\(y=\frac{3}{2}\sin(2x+\frac{\pi}{3})\)。 **三、图象对称轴与对称中心类题目** 1. **题目** - 函数\(y=\sin(2x+\frac{\pi}{3})\)的图象的对称轴和对称中心分别是什么？ 2. **答案** - 对于函数\(y = \sin(2x+\frac{\pi}{3})\)，令\(2x+\frac{\pi}{3}=k\pi+\frac{\pi}{2}\)（\(k\in Z\)），解得\(x=\frac{k\pi}{2}+\frac{\pi}{12}\)（\(k\in Z\)），所以其对称轴方程为\(x=\frac{k\pi}{2}+\frac{\pi}{12}\)（\(k\in Z\)）。 - 令\(2x+\frac{\pi}{3}=k\pi\)（\(k\in Z\)），解得\(x=\frac{k\pi}{2}-\frac{\pi}{6}\)（\(k\in Z\)），所以其对称中心为\((\frac{k\pi}{2}-\frac{\pi}{6},0)\)（\(k\in Z\)）。 <a href="/?from=ask_words" style="color:red" target="_blank">点击前往免费阅读更多精彩小说</a>

Two Zhao Pengs graduated from Sichuan University. Here is their resume: 1. Zhao Peng, male, born in June 1988, from Taizhou, Jiangsu Province. He is a lecturer at the School of Construction and the environment of Sichuan University. He is currently a full-time post-doctor in civil engineering at Sichuan University. From June to August 2013, he carried out cooperative research on the numerical simulation technology of hydraulic fracturing at the Energy Research Center of Lower Saxony, Germany. Learning and work experience: - From July 2016 to now, he has been a full-time post-doctor in civil engineering at Sichuan University. - From September 2013 to June 2016, he graduated from Sichuan University with a Ph. D. in Civil Engineering. - From September 2010 to June 2013, he graduated from Sichuan University with a master's degree in civil engineering. - From September 2006 to June 2010, he graduated from Sichuan University with a bachelor's degree in civil engineering. His main research fields were the theory and technology of hydraulic fracturing, and the dynamic performance of large-scale complex engineering structures in disaster dynamic environments. He participated in the research on the key fracturing technology for the development of the gas reservoir (Sichuan Province Science and Technology Support Plan), the research on the theory and technology of rock fracture for the reconstruction of the gas reservoir (Sichuan University-China National Petrochemicals Joint Research Project), and the experimental research on the impact resistance of the concrete shed structure and buffer material of the highway (Sichuan University-Sichuan Provincial Transportation Department Transportation Investigation, Design and Research Institute Joint Research). He had "Analysis and Design Procedure of cable-stayed bridge using advanced composite material","Study on hydraulic fracturing based on dispersed crack model","Numerical-simulation of coal and rock support fracturing under pillar-free mining conditions","Study on the cushion effect of EPE cushion shed hole under rockfall impact load" and other representative works. 2. The other was Zhao Peng, male, with a Ph.D. degree (Sichuan University, June 2017). He was a lecturer (specially hired associate professor) and a master's tutor. The main undergraduate courses were <<Water Resources>> and <<Hydro>>. Work experience: 2017.07 - 2018.01 at the School of Energy and the School of the Earth, Xihua University;2017.07 -now at the School of Forest, Sichuan Agricultural University. Work unit: School of Forest. Enrolled students: [Master's degree]:090707 Soil and Water Conservation and Desert Control;[Master's degree]:095400 Forest. E-mail: qinzhuman @ qq.com. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The reference material only mentions part of the contents of the letter. I can't get the complete original text of Harry Potter's letter. Sorry, I don't know how to answer according to the information I found. Hurry up and click on the link below to return to the super classic " Lord of Mysteries "!

At present, they only knew that Tushan Jing and Xiaoyao had a pair of twins after a hundred years of marriage. The son was named Nianliu, and the daughter was named Xiaoxiang. There was no more information about the current situation of their descendants. Had he not watched enough of Long Lovesickness 2? Hurry up and read the original work of " Everlasting Lovesickness 2: A Vow of Love "!

The following are some of the best songs related to fortune-telling in different plays: - ** The lyrics of the "Fortune Teller" from the Yue opera "Prince of the Desert"(sung by Zhao Zhigang)**: - "My heart is miserable when I hold the zither. I will calculate my own fate myself. The person sitting opposite me is my beloved. When he opened his mouth, he called her 'good miss'.' The prince's fate, listen carefully. He is a handsome and intelligent child, and a good disciple of the Xisa Royal Palace.' His parents loved him like a treasure, and the jade pendant was used as a symbol. The words 'King of the Desert' on the jade pendant would never change for thousands of years. Just as he was looking forward to more happy days, who knew that there would be a storm on the ground. Anda rebelled and was unfortunately separated from his family. The wet nurse was loyal to save the prince, and he escaped from the sword. Time passed easily, season after season. When the prince grew up to seventeen years old, the wind and sand blew against his face and he accidentally met the princess. The princess's name was Yi Li." - There was also a follow-up,"The princess is very beautiful, and the prince is very romantic. They fell in love at first sight, and their hearts were sealed." As the saying goes, all banquets in the world must end. The sound of taking care of each other was divided into two parts. They agreed to meet again next spring and shake hands. The prince was riding a white horse, and the princess was wearing a red dress. In the blink of an eye, it was spring. The prince was full of joy to visit the old days, but who knew that the scenery was still gone and that he had been snatched away to be the queen..."and other content. Through singing, he told the prince's life experience and his love story with the princess. - ** Pendant Book: Luo Cheng's Divination (sung by Zhu Qihe)**: - It included,"Every year on March 3rd, the Queen Mother meets the Eight Immortals. The Queen Mother holds a Peach Banquet, which moves 38 and 24 immortals. The Queen Mother looked up. Why didn't she see Luo Cheng's White Tiger Official? When she opened her mouth, she didn't call anyone else. When she called him Taibai, she called him Li Jinxian. I didn't ask you to subdue the demons. I asked you to go to Chang 'an and Xijing for divination. You take back the white tiger. Li Jinxian agreed, walked to the front of the immortal platform, bent down and drew a double cross. The two immortal feet stepped in the middle of the cross, pointing down three fingers at the southeast corner, drawing three times at the northwest corner, pointing three fingers, drawing three times, and the five-colored clouds fell in front of him…"The lyrics told the story background of Li Jinxian going to Chang 'an to read Luo Cheng's fortune. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The concept of " Academy City " had different settings in different works. If it was the academy city in Kazuma Sanyike's " Index of Forbidden Magic Books ", it was a place that was built with the help of Soul Chaser from the Underworld, and was built by Alesta Crowley over fifty years. It was fully managed by the " General Council ". The population was about 2.3 million, of which more than 1.8 million were students. This place had cutting-edge technology, 20 to 30 years ahead of the outside world, and was the leader of the scientific world. The students received superpower development here, and there were also seven Level5 espers. If it was the school city mentioned in the mobile game " Witch Weapon " developed by Beijing Water Qin Ling Information Technology Co., Ltd., its predecessor was a continental research institute set up by countries around the world to study the " singularity phenomenon " caused by " miracles ". Later, it gradually developed into a city of scholars. There were seven school cities here. The protagonist lived in the fifth school city, which had always maintained a neutral attitude. The city was proud of the counterattack force field defense wall Aegis. If it was the " Academy City " in other works, more information would be needed to give an accurate answer.

Five years ago, Zhao Xiao was invincible in the world. Five years later, he abandoned everything and walked down the altar to return to peace. However, a marriage agreement disrupted the peaceful life he longed for. Countless dangers and crises came one after another, including the powerful forces that dominated a region, the aristocratic families that had been passed down for hundreds of years, and the mysterious ancient families. He had no choice but to remove his disguise and continue the legend of a generation. In this story, Su Muxue and Zhao Xiao were related. The details of the plot were not given, but it was clear that they were in a story setting that was full of challenges and crises. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

The following are some ideas for writing about the observations and analysis of college students 'behavior: ** I. Introduction ** 1. ** Present the background and purpose of the observation ** - Explain why it is necessary to observe and analyze the behavior of college students. For example, the behavior of college students is an important aspect to measure the results of school education, the development of students 'quality, and the campus culture. With the development of educational concepts, a deeper understanding of college students 'behavior could help improve the quality of education and campus management. 2. ** Explain the scope and method of observation ** - It stated which groups of university students were being observed, whether they were students of specific majors, grades, or the entire school. Mention the observation methods used, such as direct observation (classroom observation, dormitory observation, etc.), survey, interview, etc., and the role of each method in obtaining information. ** 2. Observation result presented ** 1. ** Learning behavior ** - learning attitude - Description of the positive learning attitude observed, such as some students actively answering questions in class, actively participating in group discussions, seriously completing homework after class, and actively participating in extra-cursory learning activities. At the same time, they should also mention negative learning attitudes, such as playing with cell phones in class, dozing off, skipping classes, etc., and analyze the possible reasons behind these phenomena, such as whether the curriculum is unattractive, and personal motivation to learn is insufficient. - study habit - For example, some students had good time management skills and could arrange their preparation, revision, and extra-cursory activities reasonably, while some students lacked planning and crammed at the last minute. It could also mention the characteristics of learning habits in different subjects. For example, science and engineering students might do more experimental exercises, while liberal arts students paid more attention to reading and writing. 2. ** In terms of social behavior ** - interpersonal communication - This paper analyzed the interpersonal communication patterns of college students on campus, such as the relationship between students in the dormitory. Some dormitories had harmonious relationships, everyone helped each other and participated in activities together, while some dormitories had contradictions. They could also mention the characteristics of communication between students of different genders and regions, such as the differences in social circles between local students and foreign students. - Participating in clubs and group activities - Explain the situation of students participating in club activities and school collective activities. Students who actively participate may play a leading role in the club and train their organizational skills, communication skills, etc. through organizing activities; while students who do not participate may be due to lack of interest or lack of time to discuss the impact of these behaviors on the development of students 'comprehensive quality. 3. ** Living behavior ** - work habits - He described the observed habits of college students, such as some students going to bed early and getting up early to maintain a healthy pace of life, while some students stayed up late to play games and watch TV shows. He analyzed the impact of this habit on their health and learning, as well as the possible external factors, such as dormitory environment, course schedule, etc. - consuming behavior - This paper discussed the consumption patterns of college students, including basic living expenses, learning expenses, entertainment expenses, etc. For example, some students paid attention to brand consumption, while others preferred cost-effective products. It analyzed the influence of family economic factors, personal values, and social consumption culture behind different consumption behaviors. ** 3. Analysis and Reflection ** 1. ** Analysis of influencing factors ** - From the perspective of personal factors, such as personality, background, goals, and so on, the impact on behavior. For example, extroverted students may be more active in social activities, and students with better financial conditions may be more relaxed in spending. - Considering the school environment, the curriculum, the teachers, and the campus culture, it was important to shape the students 'behavior. For example, a variety of courses and excellent teachers could stimulate students 'interest in learning, and a lively campus culture was conducive to the cultivation of students' social skills. - Social and cultural factors could not be ignored, such as social trends, network culture, and other influences on college students 'behavior. For example, the popularity of online Short videos might affect students 'entertainment and time allocation. 2. ** The significance and challenge of behavior to the development of college students ** - This paper elaborated on the role of positive behavior in promoting the growth of college students, such as good learning behavior is conducive to academic progress, positive social behavior is conducive to expanding contacts and improving social skills, etc. At the same time, it pointed out the challenges brought by bad behavior, such as bad study habits that may lead to a decline in academic performance, unhealthy life behaviors that may affect physical health, etc. ** IV. Remarks and recommendations ** 1. ** Final conclusion ** - It summarized the main conclusions of the observation and analysis of college students 'behavior, emphasizing the variety and complexity of college students' behavior, as well as the characteristics of being affected by many factors. 2. ** Make a suggestion ** - As for the school, it could be suggested to improve the curriculum, improve the quality of teaching, and strengthen the construction of campus culture. For example, increase practical courses to improve students 'hands-on ability, and organize more cross-disciplinary exchange activities to broaden students' horizons. - As for college students, they should advocate the establishment of correct values and cultivate good learning and living habits. For example, encouraging students to make reasonable study plans, maintaining a healthy schedule, and rational consumption. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

Cough and chest pain could be caused by a variety of reasons, and different medications were used for different reasons. If it was cough and chest pain caused by a bacteria infection, it might need to be treated with antibiotics. However, antibiotics could not be used on their own. They had to follow the doctor's advice. Commonly used antibiotics were Moxie, cefotaime, ampicilin sulbactan, and so on. If it is caused by respiratory tract infection, rheumatism, pneumonias, etc., you can choose the following types of drugs: 1. Cough medicine: You can choose some over-the-counter anti-asthma drugs to relieve cough symptoms, such as budesuron, salbutrol, etc. 2. expectorants: Use expectorants such as bromhexine to help clear phlegm in the respiratory tract and relieve chest pain caused by coughing. 3. Pain relief medication: If the cough causes chest pain, you can use some over-the-counter medication to relieve the pain, such as ich or parkinson. In addition, acid suppressors could be used to treat cough and chest pain caused by gastroesophagus reflex disease. Because of its strong acid suppressors, high uniqueness, and long-lasting advantages, it was widely used in acid related diseases, but it also needed to be used under the guidance of a doctor. At the same time, maintaining good living habits, such as adequate rest, reasonable diet, and drinking more water, could also help alleviate the symptoms. If the symptoms persist or worsen, you should seek medical advice in time to clarify the cause so that you can carry out targeted treatment. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

From the information provided, such as "folk song accompaniment- (Guizhou lantern tune)" can be regarded as one of the old tunes of Guizhou lantern. In addition, the lantern plays of Xiaobi Buyi Miao Village, such as "Please Water,""He Qiao,""He Village Neighboring Land,""Open the Wooden Door,""Can Tai,""Can Shen,""Divide the Lights,""Picking Tea,""End,""Visit Friends,""Send Friends,""Fire Refining Pipa,""Silang Visits Mother,""(Qin) Xianglian Chuang Palace" and other related tunes also belong to the old tunes of Guizhou lantern. These old tunes have their own unique artistic characteristics. For example, some of the old tunes in the category of ground lanterns have a gentle rhythm. Free narration was stronger than lyricism, close to the recitation style, and the range of the tune was relatively narrow. When singing, it was often repeated, using the lead singer, singing in unison, and the difference between high-pitched folk songs and flat folk songs. In terms of performance, there were also a variety of unique movements such as body movements, footwork, fan movements, and handkerchief movements.