1 Memory method of high school mathematical formula
Mathematical formula is an expression method that people find some connection between things in nature and express it in some way.
2 trigonometric function
Trigonometric functions are functions, and quadrant symbols are labeled. Function image unit circle, periodic parity increase and decrease.
The same angle relation is very important, and both simplification and proof are needed. At the vertex of the regular hexagon, cut the chord from top to bottom;
The numb 1 records that triangle connecte the vertices in the center; The sum of the squares of the downward triangle, the reciprocal relationship is diagonal,
Any function of a vertex is equal to the division of the last two. The inductive formula is good, negative is positive and then big and small,
It is easy to look up the table when it becomes a tax corner, and it is essential to simplify the proof. Half of the integer multiple of two, odd complementary pairs remain unchanged,
The latter is regarded as an acute angle, and the sign is judged as the original function. The cosine of the sum of two angles is converted into a single angle, which is convenient for evaluation.
Cosine product minus sine product, angular deformation formula. Sum and difference products must have the same name, and the complementary angle must be renamed.
The calculation proves that the angle is the first, pay attention to the name of the structural function, the basic quantity remains unchanged, and it changes from complexity to simplicity.
Guided by the principle of reverse order, the product of rising power and falling power and difference. The proof of conditional equality, the idea of equation points out the direction.
Universal formula is unusual, rational formula is ahead. The formula is used in the right and wrong direction, and the deformation is used skillfully;
1 add cosine to think of cosine, 1 subtract cosine to think of sine, power-on angle is halved, and power-on and power-off is a norm;
The inverse function of trigonometric function is essentially to find the angle, first to find the value of trigonometric function, and then to determine the range of angle value;
Using right triangle, the image is intuitive and easy to rename, and the equation of simple triangle is transformed into the simplest solution set;
3 complex number
As soon as the imaginary unit I came out, the number set was expanded into a complex number. A complex number and a logarithm, the real and imaginary parts of horizontal and vertical coordinates.
Corresponding to a point on the complex plane, the origin is connected with it in the form of an arrow. The axis of the arrow is opposite to the X axis, and the resulting angle is a radial angle.
The length of the arrow shaft is a model, and the numbers are often combined. Algebraic geometric triangles, try to transform each other.
The essence of algebraic operation is I polynomial operation. The positive integer of I is the second time, and there are four numerical periods.
Some important conclusions, cleverly remember the results. The ability of mutual transformation between reality and reality is great, and complex number equals transformation.
Solve with equations and pay attention to the whole substitution. On the geometric operation diagram, the addition parallelogram,
Subtractive triangle rule judgment; Multiplication and division operations, reverse and forward rotation, expansion and contraction of annual module length.
In triangular operation, it is necessary to distinguish between radiation angle and mode. It is very convenient to take a square and make a square by using Demofo formula.
The radial angle operation is very strange, and the product quotient is used to sum the difference. These four properties are inseparable, such as equality module and yoke,
Two will not be real numbers, and the comparison size is not allowed. Complex numbers are very close to real numbers, so we should pay attention to the essential differences.
4 basic formula
Formula 1:
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2kπ+α)= sinα
cos(2kπ+α)= cosα
tan(2kπ+α)= tanα
cot(2kπ+α)= cotα
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)= -cosα
tan(π+α)= tanα
cot(π+α)= cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)= cosα
tan(-α)= -tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)= -cosα
tan(π-α)= -tanα
cot(π-α)=-coα
5 geometric memory
The trinity of point, line and surface is represented by cone billiards. All distances start from points, and all angles are made of lines.
Vertical parallelism is the key point, and the concept must be clear in the proof. Line, line, plane, plane, triple cycle.
When the whole idea of the equation is solved, it becomes consciousness. Before calculation, it is necessary to prove and draw the removed figure.
Directed line segments, straight circles, elliptic hyperbolic parabolas, polar coordinates of parametric equations and the combination of numbers and shapes are called normal forms.
Descartes' viewpoint pair, point and ordered real number pair correspond to each other, which opens up a new way of geometry.
The two ideas reflect each other and turn into ideas to fight the front line; The undetermined coefficient method is actually the idea of equations.
Summarize three types, draw a curve to solve the equation, and give the curve of the equation and the relationship between the curves.
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