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Anonymous users2024-02-11It has six basic functions (elementary basic representations):
In the planar Cartesian coordinate system xoy, a ray op is drawn from the point o, let the rotation angle be , let op=r, and the coordinates of the p point are (x,y).
The sine function sin = y r
Cosine function cos =x r
Tangent function tan =y x
Cotangent function cot = x y
The secant function sec = r x
Cosecant function csc =r y
The hypotenuse is r, the opposite edge is y, and the adjacent edge is x. ）
and two functions that are not commonly used and tend to be obsolete:
Positive vector function versin =1-cos
Co-vector function covers =1-sin
Sine (sin): The opposite side of the angle is more hypotenuse than the upper side.
Cosine: The adjacent edge of the angle is more hypotenuse than the upper side.
Tangent (tan): The opposite side of the angle is more than the adjacent edge.
Cotangent (cot): The adjacent edge of the angle is compared to the opposite edge.
secant: The hypotenuse of the angle is greater than the adjacent edge.
Cosecant (csc): The hypotenuse of the angle is more than the top side.
This paragraph] basic formula.
Isoangular trigonometric relation.
Square relation: sinx) 2+(cosx) 2=11 (tanx) 2 (secx) 2
1＋(cotx)^2＝(cscx)^2
The relationship between the product: sin = tan cos
cosα=cotα×sinα
tanα=sinα×secα
cotα=cosα×cscα
secα=tanα×cscα
cscα=secα×cotα
Reciprocal relation: tan cot 1
sinα ·cscα＝1
cosα ·secα＝1
Quotient relationship: sin cos tan sec csc cos sin cot csc sec In a right triangle ABC, the sine of angle A is equal to the opposite side of angle A than the hypotenuse, and the cosine is equal to the adjacent side of the angle A than the hypotenuse.
Tangent is equal to the opposite side of the adjacent side, symmetry.
The terminal edge of 180 degrees- and the terminal edge of are symmetrical with respect to the y-axis.
The terminal edge of and the terminal edge of are symmetrical with respect to the x-axis.
The terminal edge of 180 degrees+ and the terminal edge of are symmetrical with respect to the origin.
The terminal edge of 180 degrees 2- is symmetrical with respect to y=x.
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Anonymous users2024-02-10The basics of trigonometric functions lie in the relationship between the three sides.
sin=Opposite edge: hypotenuse.
cos=adjacent edge: hypotenuse.
tan=opposite edge: adjacent edge.
These three are commonly used.
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Anonymous users2024-02-09Trigonometric function is one of the basic elementary functions, and Zaoxunchen is a function with the angle as the independent variable, and the angle corresponds to the coordinates of the intersection point of the terminal edge of any angle and the intersection of the Shan Chang rubber position circle or its ratio as the dependent variable. It can also be defined equivalently in terms of the length of the various linear segments related to the unit circle.
Trigonometric functions play an important role in the study of the properties of geometric shapes such as triangles and circles, and are also a fundamental mathematical tool for the study of periodic phenomena. In mathematical analysis, trigonometric functions are also defined as infinite series or solutions to specific differential equations, allowing their values to be extended to arbitrary real values, even complex values.
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Anonymous users2024-02-08sin 0°90°180°270°360° value 0 1 0 -1 0
COS 0°90°180°270°360° value 1 0 -1 0 1
tan 0°90°180°270°360° value 0 0 0
COT 0°90°180°270°360° value 0 0
It means that there is no such thing, and each value corresponds to the angle, so it will be clearer to draw an image.
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Anonymous users2024-02-07Right triangle definition.
It has six basic functions (elementary basic representations) :( the hypotenuse is r, the opposite edge is y, and the adjacent edge is x. In the planar Cartesian coordinate system xoy, a ray op is drawn from the point o, let the rotation angle be , let op=r, and the coordinates of the p point are (x,y).
Sine function sin = y r sine (sin): the opposite side of the angle than the hypotenuse.
Cosine function cos = x r cosine (cos): The adjacent edge of the angle is more than the hypotenuse.
Tangent function tan = y x tangent (tan): the opposite side of the angle is relative to the adjacent edge.
Cotangent function cot = x y cotangent (cot): the adjacent edge of the angle is compared to the opposite edge.
secant function sec = r x secant (sec): the hypotenuse of the angle is relative to the adjacent edge.
Cosecant function csc = r y cosecant (csc): the hypotenuse of the angle compared to the opposing edge.
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Anonymous users2024-02-06The derivative of sinx is cosx, and the derivative of cosx is -sinx.
The derivative of tanx is sec x=1 cos x=1+tan x.
Indefinite integrals The result is not a unique derivative, and the verification should be able to improve the computational power of the differential calculation.
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Anonymous users2024-02-05Trigonometric function is one of the basic elementary functions, which is a function with angle as the independent variable, and the angle corresponds to the coordinate of the intersection point of the terminal edge of any angle with the unit circle or its ratio as the dependent variable.
<> as shown in the figure above, the sine function sin is positive in one or two quadrants, the cosine function cos is positive in one and four quadrants, and the tangent function tan is positive in one and three quadrants (one perfect sine, two sine sine, three tangent, four cosine).
<> made it several times, and it always showed an operation error, so I sent a screenshot directly) <>
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Anonymous users2024-02-04sin 0°90°180°270°360° value denier bend 0 1 0 -1 0
COS 0°90°180°270°360° value 1 0 -1 0 1
tan 0°90°180°270°360° value 0 0 0
COT 0°90°180°270°360° value 0 0
It means that it does not exist, and each value corresponds to the angle search, and the image of the painting will be clearer.
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Anonymous users2024-02-03The most commonly used trigonometric functions are: sin0=0 cos0=1 sin30=1 2 cos30= 3 2 sin45= 2 2 cos45= 2 2 sin60= 3 2 cos60=1 2 sin90=1 cos90=0 sin180=0 cos180=-1 tan0=0 tan30= 3 3 tan45=1 tan60= 3 tan180=0 Trigonometric functions are functions in mathematics that belong to the transcendent function of elementary functions. Their essence is a mapping between a set of any angles and a set of variables with a ratio of values.
The usual trigonometric functions are defined in a planar Cartesian coordinate system. It defines the entire field of real numbers. Another definition is in a right triangle, but not completely.
The most basic trigonometric formula: Reciprocal relation: tan ·cot =1 sin ·csc =1 cos ·sec =1 quotient relation:
sin cos =tan =sec csc cos sin =cot = csc sec squared relationship: sin 2( )cos 2( )=1 1+tan 2( )=sec 2( )1+cot 2( )=csc 2( ).
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