The knowledge point of a basic elementary function, a compulsory math course for senior one, leads a line from a vertex to an edge and passes through a certain point on the other side, then this figure becomes two triangles, with a common edge and another group of edges on the same straight line. There are six internal angles, each of which is the internal angle of a triangle and the external angle of another triangle.
In addition, there are angles larger than right angles and smaller than rounded corners.
Sine function? =y/r
Cosine function cos? =x/r
Tangent function tan? =y/x
Cotangent function cot? =x/y
Sec secant function? =r/x
Cotangent function csc? =r/y
The basic relationship between trigonometric functions with the same angle;
? Square relation:
sin^2(？ )+cos^2(？ )= 1
tan^2(？ )+ 1=sec^2(？ )
cot^2(？ )+ 1=csc^2(？ )
? Product relationship:
Sin? = Tan? * Because?
Because? =cot？ * sin?
Tan? = sin? * seconds?
A cot? =cos？ *csc？
sec？ = Tan? *csc？
csc？ = seconds? *cot？
? Reciprocal relationship:
Tancott. = 1
sincsc？ = 1
cossec？ = 1
When the arc length and radius of a circle are equal, the corresponding angle is 1 radian. The conversion relationship between radian and angle is radian * 180/(2*? ) = Angle
★ Inductive formula ★
Commonly used inductive formulas have the following groups:
Formula 1:
Settings? For any angle, the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2k？ +? ) = sin?
cos(2k？ +? )=cos？
Tan (2k? +? ) = Tan?
cot(2k？ +? )=cot？
Equation 2:
Settings? For any angle, +? What is the trigonometric function value of? sin(？ +? ) =-sin?
cos(？ +? )=-cos？
Tan (? +? ) = Tan?
cot(？ +? )=cot？
Formula 3:
Any angle? Use-? The relationship between trigonometric function values is:
Sin (-? ) =-sin?
cos(-？ )=cos？
Tan (- ) =-Tan?
cot(-？ )=-cot？
Equation 4:
Can be obtained by Formula 2 and Formula 3? -? With what? sin(？ -? ) = sin?
cos(？ -? )=-cos？
Tan (? -? ) =-Tan?
cot(？ -? )=-cot？
Formula 5:
Using the first-order equation and the third-order equation, we can get 2? -? With what? The relationship between trigonometric function values: sin(2? -? ) =-sin?
cos(2？ -? )=cos？
Tan (2? -? ) =-Tan?
cot(2？ -? )=-cot？
Equation 6:
? /2 and 3? /2 and? The relationship between trigonometric function values is:
Sin (? /2+? )=cos？
cos(？ /2+? ) =-sin?
Tan (? /2+? )=-cot？
cot(？ /2+? ) =-Tan?
Sin (? /2-? )=cos？
cos(？ /2-? ) = sin?
Tan (? /2-? )=cot？
cot(？ /2-? ) = Tan?
Sin (3? /2+? )=-cos？
cos(3？ /2+? ) = sin?
Tan (3? /2+? )=-cot？
cot(3？ /2+? ) =-Tan?
Sin (3? /2-? )=-cos？
cos(3？ /2-? ) =-sin?
Tan (3? /2-? )=cot？
cot(3？ /2-? ) = Tan?
(above k? z)
Function Type First Quadrant Second Quadrant Third Quadrant Fourth Quadrant Sine++Cosine++Tangent+? + ? cotangent
Properties of sine function:
Analytical formula: y=sinx
draw
Waveform image (obtained by projecting the unit circle into the coordinate system)
Domain of definition
R (real number)
Scope:
[- 1, 1] Maximum value: ① Maximum value: When x= (? /2)+2k？ , y(max)= 1 ② minimum value: when x=- (? /2)+2k？ , y(min)=- 1 value point: (k? ,0)
Symmetry:
1) Symmetry axis: About the straight line x= (? /2)+k？ Symmetry 2) Central symmetry: About the point (k? 0) Symmetry period: 2?
Parity check:
odd function
Monotonicity:
In [-(? /2)+2k？ ,(? /2)+2k？ ] is an incremental function, in [(? /2)+2k？ ,(3? /2)+2k？ ] is a subtraction function.
Properties of cosine function:
cosine function
Picture:
Waveform image
Domain: r
Range: [- 1, 1]
Maximum value:
1) when x=2k? ，y(max)= 1。
2) When x=2k? +? ，y(min)=- 1。
Zero point: (? /2+k？ ,0)
Symmetry:
1) Symmetry axis: About the straight line x=k? symmetrical
2) Central symmetry: About the point (? /2+k？ 0) Symmetry
Period: 2?
Parity: even function
Monotonicity:
In [2k? -? ，2k？ ] is an incremental function.
In [2k? ，2k？ +? ] is a subtraction function.
Domain: {x|x? (? /2)+k？ ，k？ Z}
Scope: r
Maximum: There are no maximum and minimum values.
Zero point: (k? ,0)
Symmetry:
Axisymmetric: There is no axisymmetric.
Central symmetry: about the point (k? 0) Symmetry
Period:
Parity check: odd function
Monotonicity: in (-? /2+k？ ,? /2+k？ ) They are all adding functions.
Mathematics learning method in senior one: 1. Strengthen independent preview.
Preview should be: intensive reading, intensive reading and rough reading. The so-called close reading means reading the textbook carefully, and recording some important contents or instant inspiration or ideas with a pen while reading. Read carefully, including punctuation and border content, read, think, etc., and don't miss a word. It is best to write out the meaning of each paragraph, of course, including after-school exercises and exercises to be done independently, and you can mark the questions that you can't meet; Intensive reading is to mark the key contents of the book after careful reading, and then take a closer look and think about it; On the basis of intensive reading and intensive reading, rough reading is to quickly browse the content of self-study and think about what you have learned and what you should pay attention to.
Second, keep up with the rhythm of the lecture.
Autonomous preview is the basis of listening to a good lesson. It is not difficult to listen to a good lesson as long as you prepare well. The common feature of high school teachers' lectures is their fast pace. The teacher will ask us to review and preview as much as possible. Because teachers have to reprocess a lot of knowledge in books when they are in class. In this way, class has become the most critical link, and walking for a while may make you have a bunch of blind spots in your understanding! So listen carefully in class, think actively according to the teacher's ideas, and of course take notes. Notes are not copied from the blackboard, they should be the key points. Add your own understanding or confusion, and supplement your notes in time so that you can review and sort them out later.
Third, think independently about homework.