"The second answer is from [0,2π), cosπ/3=cos5π/3=1/2, combined with the cosine line, we can get the solution set of cosα≤1/2. The most difficult part is actually the third
It is known that within [0,2π), |sinπ/4|=|cosπ/4|=|sin3π/4|=|cos3π/4|=|sin5π/4|=|cos5π/4|=|sin7π/
4｜=｜sin7π/4｜=√2￣/2, combining cosine and sine lines, so the solution set of |cosα｜＞｜sinα｜ is {α｜kπ-π/4＜α＜kπ+π/4
,k∈Z}, you see, is it very simple?”
After finishing the whole paragraph, Yu Hua panted slightly. After explaining the problem-solving ideas, he finally felt like a high school mathematics teacher. His throat hurt after giving a class.
"..."
The thin boy sitting next to him looked at the draft paper and then at Yu Hua's breathing, his face full of confusion.
Simple?
This thing can really be called, simple???
Looking at the densely packed draft paper, the thin boy's mind was full of a series of question marks. He really couldn't muster the courage to regard this draft paper full of incomprehensible articles as simple.
He couldn't understand the questions written above, and the questions above also looked down upon him, a poor student.
"Uh, did I speak too fast?" Yu Hua came back to his senses. Seeing the appearance of the thin boy, he scratched his head. He was a little embarrassed and felt very guilty in his heart: "I speak faster, and many steps can be simplified directly.
No, I'm sorry."
I'm really sorry. I have been born in two lifetimes and have never been a top student. It seems that I shouldn't simplify many necessary details.
The thin boy came back to his senses, looked at Yu Hua with a guilty face, lowered his head and apologized: "I'm sorry, I was too stupid."
"No, if not, just practice more on this kind of questions. Come on, come on, I will continue to teach you. Look at this question, there are three questions in total. The first and second questions are relatively simple. We just
You need to draw a trigonometric function line to find it. The third question is more complicated and involves the feasible region. It is not easy to draw here. There are three drawing methods in total. I will teach you the simplest drawing method..." Yu Hua shook his head.
There is no fool who can go to Peking No. 4 Middle School. The only difference lies in whether the foundation is solid. Speak calmly and start from the beginning.
Is it appropriate to help others to the end without forming a classmate relationship?
This is inappropriate.
As a young man striving towards the goal of academic excellence, it is fundamental to help students with lower grades to move forward.
Seeing Yu Hua with a serious face, the thin boy was startled for a moment, and quickly concentrated on listening carefully. He held a scratch paper and pen in his right hand and wrote down the problem-solving methods described by Yu Hua.
From the solution to the first question to the solution to the third question, Yu Hua gives the formula and process of each step in detail, and then gives the reason why this formula should be used, as well as the content of each formula of the trigonometric function line, the thin boy
Like the most sincere student, he kept nodding and recording.
After a while.
"Classmate Yu Hua, thank you so much. I didn't understand this question when Mr. Ren, my superior, talked about it last time. After listening to you talk about it this time, I finally understand it, Niu." I received three pieces of draft paper and
The thin student who solved the final question felt that the whole world of learning seemed to have opened a new door. He stood up and bowed to Yu Hua to express his gratitude, his face full of gratitude.
This final problem of the solution of inequalities of trigonometric functions and lines that eluded him was finally solved. The key thing is that he mastered the solution to this problem.
Although, according to Yu Hua, this is the simplest one.
But this is enough.
"It's okay, I just did what a high school student should do." He received praise and gratitude from his thin classmates. Although there was no substantial reward, Yu Hua was very happy and smiled all over his face.
One word, comfortable.
It turns out that this is what it feels like to be a top student.
"Classmate Yu Hua, I have a heartfelt request. Can you teach me other knowledge points of trigonometry? Trigonometric function lines prove trigonometric function inequalities, the domain of trigonometric functions and trigonometric identity transformations are all my weaknesses.
"The thin boy's eyes showed a trace of expectation. He looked at the humble and confident Yu Hua with an embarrassed look on his face: "I..."
At this moment, before the thin classmate could finish speaking, Yu Hua's face froze when he heard this tone, and the smile on his face disappeared instantly. He quickly stopped and rattled a rejection: "Wait... I'm sorry, classmate, I have a heavy workload, so I can't do it for the time being.
I don’t have time to teach, and I don’t learn much.”
Teach other knowledge points?
Yu Hua is not prepared to do such a thankless job. He also has to study mathematics, strive for perfect scores, go to see Hua Luogeng, and study the three courses of physics, chemistry, and biology, so he has no time to teach his classmates.
Help your classmates when it's time to help them, and defend your own interests when it's time to do so.
Time cannot be wasted!
After finishing his words, just when Yu Hua had already thought of the second way to refuse, he heard the weak and unconfident words of another thin boy in his ears: "I...I can give you thirty dollars in return.
.”
After speaking without any confidence, the thin boy lowered his head.
"I really don't have time..." Yu Hua was about to say the second word of rejection. Just three words came out of his throat, and suddenly he found that his throat seemed to be restrained by some invisible force and he was speechless. He was startled for a moment, and then he came to his senses.
, a little confused.
What did I hear?
On top of the horse column, I seem to hear the call of dear silver dollar?
"Wait, you mean, thirty yuan?" Yu Hua's eyes widened, looking at the thin boy who lowered his head and felt inferior, and he suspected that he had heard wrong.
"I'm sorry, classmate Yu Hua, I... I only have so much New Year's money this year, is that okay?"
Hearing Yu Hua's voice, the thin boy lowered his head and stuttered a little. He didn't dare to look up at Yu Hua's expression. He knew that thirty dollars would not solve the problem. He looked extremely inferior. He wanted to improve his grades but didn't want to pay.
The price, there is no such good thing in the world.
ashamed.
Uncomfortable.
The money is not enough, he knows.
But he really had no choice. He only had thirty yuan left at his disposal, which was still this year's lucky money.
"Gulu."
Swallowing his saliva, Yu Hua looked at the thin boy with a face full of inferiority in front of him, recalling the other person's words in his ears, and kept persuading himself to be steady. His right hand trembled slightly, and he tried to control it, and patted the thin boy on the shoulder: "Yes, of course.
...Helping my classmates improve and improve their grades is what I should do."
There was even some trembling between words.
Gan!
What kind of family is this? They only have 30 yuan in lucky money!!!
For the sake of Yin Yuan's face, ah no, for the sake of helping his classmates improve and improve their grades, he did this tutoring thing.
As for time?
As the saying goes: time is money.
"Really?" Upon hearing Yu Hua's answer, the thin boy immediately raised his head with a look of surprise on his face.