Memory formula of trigonometric function and differential product formula
1. Memory of sum and difference of two angles of sine and cosine formulas
Sin(A+B)=sinAcosB+cosAsinB。
Cosine with the same name is different, cos(A+B)=cosAcosB-sinAsinB.
A comes first and B comes last.
Second, the memory of product sum and difference and product sum and difference formula
Product sum and difference formula:
Sinkos? =( 1/2)[sin(？ +? )+sin(？ -? )] sine addition after positive negative.
Cousin? =( 1/2)[sin(？ +? )-sin (? -? )] Positive sine difference between the former and the latter
coscos？ =( 1/2)[cos(？ +? )+cos(？ -? )] cosine addition of remainder value
Xin Xin? =-( 1/2)[cos(？ +? )-cos(？ -? )] Total positive cosine difference
Sum-difference product formula:
Sin? +sin? =2sin[(？ +? )/2]cos[(？ -? ) /2] Sine before sine plus sine
Sin? Sin? =2cos[(？ +? ) /2] sin [(? -? ) /2] Sine minus sine cosine is in front.
Because? +cos？ =2cos[(？ +? )/2]cos[(？ -? ) /2] Cosine and Cosine are both Cosines.
Because? Because? =-2sin[(？ +? ) /2] sin [(? -? ) /2] cosine subtraction cosine sign change correction string
Tips for memorizing mathematical knowledge points
1 classified memory method
According to the nature, characteristics and internal relations of memory materials, it helps students to remember a lot of knowledge. For example, after learning the unit of measurement, everything you have learned can be summarized into five categories: length units; Area unit; Volume and unit of volume; Weight unit; Time unit. This classification can easily systematize, organize and memorize complex things.
2 Song formula mnemonic method
It is to compile the mathematical knowledge to be memorized into songs, formulas or jingles for easy memorization. For example, to measure the angle, you can compose several songs: put the protractor on the angle, align the center with the vertex, point the zero line to one side, and look at the degree on the other side. ? For another example, the movement of the decimal point position leads to the change of the number size. Decimal point, please follow me. You have to find the right place to go, okay? Left? And then what? Right? ; The horizontal belt is a you, it expands to you; Add a left horizontally and narrow it to the left; Ten times, one step, a hundred times, two steps, not enough digits to find? 0? Hook. ? In this way, students not only like to remember, but also remember well.
3 regular memory method.
That is, according to the internal relations of things, find out the regular things to remember. For example, memory length unit, area unit, unit of volume transformation method and aggregation method. Chemical method and aggregation method are opposite to each other, that is, higher unit value? Propulsion rate = low-level unit value, low-level unit value? Advanced rate = value of advanced unit. Mastering these two laws will solve the problem of chemical polymerization. Regular memory requires students to process and sort out the relevant materials they have learned with their brains, so the memory is firm.
4 list memory method
It is to list some confusing memory materials into tables to achieve the purpose of memory. This method is obvious, intuitive and comparative. For example, to remember the differences between the three concepts of prime number, prime factor and coprime number, you can make a table to help students remember.
5-key memory method
With the growth of age, students learn more and more mathematical knowledge, so it is a waste of time and a bad memory effect for students to remember comprehensively. Therefore, in order to make students learn to remember the key contents, students can remember other contents through deduction and association on the basis of remembering the key contents. For example, learn the common quantitative relationship: work efficiency? Working hours = workload. Workload? Work efficiency = working hours; Workload+working hours = working efficiency. As long as you remember the first quantitative relationship, you can deduce the last two quantitative relationships from the multiplication and division relationship. This way of memory reduces students' memory burden and improves memory efficiency.
Effective memory method of mathematical knowledge points
1, addition of rational numbers: addition with the same sign is one-sided; Different symbols add "big" and subtract "small", and the symbols follow big; Absolute values are equal, "zero" is just right. [Note] "Big" minus "Small" refers to the absolute value.
2. Merge similar items: Merge similar items, and the rules should not be forgotten, just seek the sum of coefficients, and the letters and indexes remain unchanged.
3. Rules for removing brackets and adding brackets: The key to removing brackets and adding brackets is to look at symbols. The parentheses are preceded by a plus sign, and the parentheses remain unchanged. The parentheses are preceded by a minus sign, and both parentheses have changed.
4. Unary linear equation: known unknowns should be separated by shifting, adding and subtracting shifting terms should be changed, and multiplication and division should be reversed.
5, identity transformation: two numbers are subtracted, the most common exchange position, positive and negative only depends on its index, odd numbers become even numbers unchanged. (a-b)2n+ 1 =-(b-a)2n+ 1(a-b)2n =(b-a)2n
6. Square difference formula: There are two square difference formulas. Remember that the symbols are opposite, multiply the beginning and end by the end, and don't confuse it with the complete formula.
7. Perfect Square: There are three perfect squares, the first and last symbols are fellow villagers, the first and last squares, and the first and second squares are placed in the middle; First of all? The closing bracket is square, and the final bullet follows the center.
8. factorial decomposition: the first mention (common factor) and the second set (formula) are divided into three groups. It makes sense to look at a few items carefully. Two terms only use square difference, three terms are cross multiplication, and the array method is skillful and not sloppy. Look at the four items carefully. If there are three square numbers (items), use one or three groups, otherwise use two or two groups, five or six items are more, and two or three try to group.
9. "substitution": dig out the letters and replace them with numbers (formulas), and both numbers and letters are kept; Replace with fractions or negative numbers, enclose them in parentheses, put (present) brackets in the original brackets, and gradually change brackets (small-medium-large).
Single operation: addition, subtraction, multiplication and division (on), three-level operation is clear, coefficient is calculated at the same level, and exponential operation is degraded.
10, the general steps to solve the problem of linear inequality in one variable: remove the denominator and brackets, change the sign when moving items, merge similar items, and then remove the coefficients. Don't forget to change the direction of inequality when both sides are divided by (divided by) negative numbers.
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