Acute angle formula of trigonometric function in formulas of trigonometric functions Daquan of senior high school
Opposite side/hypotenuse of sinα=∞α;
Adjacent side/hypotenuse of cosα=∞α;
Opposite side of tan α = adjacent side of ∠ α/∠α;
Adjacent side of cot α = opposite side of ∠ α/∠α.
Double angle formula
Sin2A = 2SinACosA
cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1；
tan2A=(2tanA)/( 1-tanA^2)。
(Note: Sina 2 is the square of Sina 2 (a))
Triple angle formula
sin 3α= 4 sinαsin(π/3+α)sin(π/3-α)；
cos 3α= 4 cosαcos(π/3+α)cos(π/3-α)；
tan3a = tan a tan(π/3+a) tan(π/3-a).
Derivation of triple angle formula
sin3a = sin(2a+a)= sin 2 acosa+cos 2 asina .
Auxiliary angle formula of trigonometric function
Asinα+bcosα = (A2+B2) (1/2) sin (α+t), where
sint=b/(a^2+b^2)^( 1/2)；
cost=a/(a^2+b^2)^( 1/2)；
tant = B/A；
asinα+bcosα=(a^2+b^2)^( 1/2)cos(α-t),tant=a/b。
Reduced power formula
sin^2(α)=( 1-cos(2α))/2=versin(2α)/2；
cos^2(α)=( 1+cos(2α))/2=covers(2α)/2；
tan^2(α)=( 1-cos(2α))/( 1+cos(2α))。
Expanding reading: how to learn high school mathematics to learn to read textbooks well and learn to study.
Some students who "feel good about themselves" often despise the study and training of basic knowledge, skills and methods in textbooks. They often forget what to do, but they are interested in difficult problems to show their "level". They aim too high, value "quantity" over "quality" and fall into the ocean of problems. They either make mistakes in calculation or give up halfway in formal homework or exams. Therefore, students should start from the first year of high school and enhance their awareness of learning from textbooks. We can treat every theorem and every example as an exercise, carefully re-prove, re-solve, and add some comments appropriately, especially through the explanation and analysis of typical examples. Finally, we should abstract the mathematical ideas and methods to solve such problems, do a good job of reflection after solving problems in writing, and summarize the general and special laws of solving problems in order to popularize and flexibly use them. In addition, students should solve problems independently as much as possible, because the process of solving problems is also a process of cultivating the ability to analyze and solve problems, and it is also a process of research.
Take notes and listen carefully in class.
First of all, it is very important to cultivate good listening habits in classroom teaching. Of course, listening is the main thing. Listening can help you concentrate. You should understand and listen to the key points of the teacher. Pay attention to thinking and analyzing problems when listening, but only listening without remembering, or just remembering without listening, it is inevitable to pay attention to one thing and lose sight of another, and the classroom efficiency is low. Therefore, we should take notes appropriately and purposefully to understand the main spirit and intention of the teacher in class. Scientific notes can improve the efficiency of a 45-minute class.
Thirdly, if there is no certain speed in math class, it is ineffective learning. Slow learning can't train the speed of thinking, the agility of thinking and the ability of mathematics, which requires that mathematics learning must have rhythm, so that over time, the agility of thinking and the ability of mathematics will gradually improve.
Finally, in math class, teachers usually ask questions and perform them, sometimes accompanied by discussion, so they can hear a lot of information. These questions are very valuable. For those typical problems, problems with universality must be solved in time, and the symptoms of the problems cannot be left behind or even solved. Valuable problems should be grasped in time, and the remaining problems should be supplemented in a targeted manner and pay attention to practical results.
Do your homework and pay attention to norms.
It is also necessary to cultivate good homework habits in classroom and extracurricular exercises. In homework, we should not only be neat and tidy, but also be orderly, which is an effective way to cultivate logical ability and must be done independently. At the same time, it can cultivate a sense of responsibility to think independently and solve problems correctly. When doing homework, we should advocate efficiency, and homework that should be completed in ten minutes should not be delayed for half an hour. Tired homework habits make the thinking loose and the energy unfocused, which is harmful to the cultivation of mathematical ability. To master the study habits of mathematics, we must start from the first year of high school and cultivate the study habits from the psychological characteristics of age growth and the requirements of different learning stages.
Write a summary and grasp the law.
A person can constantly improve by constantly accepting new knowledge, encountering setbacks, having doubts and summing up. "Students who can't summarize will not improve their ability, and frustration experience is the cornerstone of success." The biological evolution process of survival of the fittest in nature is the best example. Learning should always sum up the rules, with the aim of further development. Through the usual contact and communication with teachers and classmates, the general learning steps are gradually summarized, including: making a plan, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and extracurricular learning, which are simply summarized as four links (preview, class, sorting and homework) and one step (review summary). Each link has profound content, strong purpose and pertinence, and should be put in place. Adhere to the study habit of "two before and two after a summary" (preview first, then listen to lectures, review first, then do homework, and write a summary of each unit).