Definition of acute angle trigonometric function
The sine (sin), cosine (cos) and tangent (tan), cotangent (cot), secant (sec) and cotangent (csc) of acute angle A are all called acute trigonometric functions of angle A.
Sine equals the hypotenuse of the opposite side.
Cosine is equal to the ratio of adjacent side to hypotenuse.
The tangent is equal to the opposite side of the adjacent side.
Cotangent equals the comparison of adjacent edges.
Secant is equal to the hypotenuse than the adjacent edge.
Cotangent is equal to the hypotenuse compared to the edge.
Tangent and cotangent are reciprocal.
Its essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.
Because of the periodicity of trigonometric function, it does not have the inverse function in the sense of single-valued function.
It has six basic functions (elementary basic representation):
Function name sine cosine tangent cotangent secant cotangent
In the plane rectangular coordinate system xOy, draw a ray OP from point O, and the rotation angle is? Let OP=r and the coordinate of point p be (x, y).
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 hypotenuse is R, the opposite side is Y, and the adjacent side is X ...)
And two functions that are not commonly used and easily eliminated:
Positive vector function version? = 1-cos？
Covector functions include? = 1-sin？
The 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? =tancos？
Because? =cotsin？
Tan? =sinsec？
A cot? =coscsc？
sec？ =tancsc？
csc？ =seccot？
? Reciprocal relationship:
Tancott. = 1
sincsc？ = 1
cossec？ = 1
In the right triangle ABC,
The sine value of angle a is equal to the ratio of the opposite side to the hypotenuse of angle a,
Cosine is equal to the adjacent side of angle a than the hypotenuse.
The tangent is equal to the opposite side of the adjacent side,
Cotangent equals the comparison of adjacent edges.
The relationship between trigonometric functions of complementary angles;
Sin (90? -? )=cos？ ，cos(90？ -? ) = sin? ,
Tan (90? -? )=cot？ ，cot(90？ -? ) = Tan? .
Related articles:
1. Reflections on the simple application teaching of acute trigonometric function in ninth grade mathematics
2. The third math tutorial video: acute trigonometric function
3. The ninth grade math teacher work plan
4. Reflections on the work of junior high school math teachers
5. Guidance and summary of mathematics learning methods in senior two.