1. How to learn the inverse trigonometric function

To learn the inverse trigonometric function well, we must first understand the principal value interval, and only in the principal value interval can trigonometric function and inverse trigonometric function correspond to each other one by one. Secondly, in order to understand the relationship between trigonometric function and norm trigonometric function, many conclusions about inverse trigonometric function must be solved by trigonometric function. Thirdly, many practical problems can often be solved by the periodicity of trigonometric function and the addition and subtraction of a certain value in the indicating interval of inverse trigonometric function. Understand that the inverse trigonometric function is just one of the many inverse functions of trigonometric function.

2. Have you ever learned the inverse trigonometric function? Thank you very much.

I sorted out some useful things for high school students from the internet, hoping to help you.

It is the general name of the functions of arcsine x, arccosine, arctangent, arctangent x and arctangent x, which respectively represent the angles at which sine, cosine, tangent and cotangent are x.

The inverse function of (1) sine function y=sin x on [-π/2, π/2] is called an arcsine function. The arcsine x represents the angle with the sine value of x, and the value range of the angle is in the range of [-π/2, π/2].

⑵ The inverse function of cosine function y=cos x on [0, π] is called anti-cosine function. Arccos x represents the angle whose cosine is x, and the range of the angle is within the interval of [0, π].

(3) The inverse function of the tangent function y=tan x on (-π/2, π/2) is called the arc tangent function. Arctan x represents an angle whose tangent is x, and the value range of the angle is within the range of (-π/2, π/2).

There are three main inverse trigonometric functions:

Y=arcsin(x), domain [- 1, 1], range [-π/2, π/2]

Y=arccos(x), domain [- 1, 1], range [0, π].

Y=arctan(x), domain (-∞, +∞), range (-π/2, π/2).

Y=arccot(x), domain (-∞, +∞), range (0, π).

Sin(arcsin x)=x, domain [- 1, 1], range [- 1, 1] arcsin (-x) =-arcsinx.

PS: The relationship between inverse trigonometric function and trigonometric function is the same as that between function and inverse function. In the principal value interval, the domain of trigonometric function is the domain of inverse trigonometric function, and the domain of trigonometric function is the domain of inverse trigonometric function.

Hope to adopt! ^_^

3. Solve the inverse function of inverse trigonometric function in detail.

Because trigonometric functions are not monotone functions in the whole domain.

So there is no inverse function.

So the inverse trigonometric function is not the inverse of trigonometric function.

It's just that we define a domain of trigonometric function, and trigonometric function is monotonous in this range.

There is an inverse function at this time.

Is an inverse trigonometric function.

4. Inverse trigonometric function

Let the lengths of three sides be a, b and c respectively.

According to cosine theorem

cosA=(b^2+c^2-a^2)/2bc

A=arccos[(b^2+c^2-a^2)/2bc]

You can get it in the same way.

B=arccos[(a^2+c^2-b^2)/2ac]

C=arccos[(a^2+b^2-c^2)/2ab]

If in doubt, please ask.

Satisfied, please adopt.

If you have any other questions, please adopt this question and ask for help.

It's not easy to answer questions, hope to cooperate.

I wish you progress in your study O(∩_∩)O

5. Calculator inverse trigonometric function

Inverse trigonometric function is a basic elementary function. It is the general name of the functions of arcsine x, arccosine, arctangent x, arccosine x, arccosine x, arccosine x, arccosine x, arccosine x, and arccosine x, which respectively represent the angles of arcsine, arccosine, arctangent and arctangent.

The inverse function of trigonometric function is a multi-valued function, because it does not meet the requirement that the independent variable corresponds to a function value, and its image is symmetrical with its original function about function y = X. Euler put forward the concept of inverse trigonometric function, and expressed it in the form of "arc+function name" for the first time.

(5) Extended reading of anti-trigonometric function network course:

In order to make the interval determined by the single-valued inverse trigonometric function representative, the following conditions are often observed:

1, in order to ensure that the function corresponds to the single value of the independent variable, the determined interval must be monotonous;

2. It is best that the function is continuous in this interval (the reason why it is best here is because the arc tangent and anti-cotangent functions are discontinuous);

3. For the convenience of research, it is often required that the selected interval includes the angle from 0 to π/2;

4. Make sure that the function value domain on the interval should be the same as the definition domain of the whole function. The inverse trigonometric function thus determined is single-valued. In order to distinguish it from the multi-valued inverse trigonometric function above, the notation of a in arc is often changed to a, for example, the single-valued arcsine function is recorded as arcsin X.

6. What is an inverse trigonometric function?

Inverse trigonometric function is a basic elementary function. Is the floorboard of functions such as arcsine x, arccosine arccos x, arctangent arctan x, arccot x, arcsec x, arccsc x, which respectively represent the angles of arcsine, arccosine, arctangent, anti-cotangent, arctangent and anti-cotangent.

The inverse function of trigonometric function is a multi-valued function, because it does not meet the requirement that the independent variable corresponds to a function value, and its image is symmetrical with its original function about function y = X. Euler put forward the concept of inverse trigonometric function, and expressed it in the form of "arc+function name" for the first time.

(6) Extended reading of anti-trigonometric function network course

Usually follow the following conditions:

1, in order to ensure that the function corresponds to the single value of the independent variable, the determined interval must be monotonous;

2. The function is preferably continuous in this interval (the reason why it is best here is because the arctangent and anti-cotangent functions are more precise);

3. For the convenience of research, it is often required that the selected interval includes the angle from 0 to π/2;

4. Make sure that the function value domain on the interval should be the same as the definition domain of the whole function. The inverse trigonometric function thus determined is single-valued. In order to distinguish it from the multi-valued inverse trigonometric function above, the notation of a in arc is often changed to a, for example, the single-valued arcsine function is recorded as arcsin X.

7. When do you learn the inverse trigonometric function?

At the end of the chapter on trigonometric functions

Let's go to high school next semester.

8. What is an inverse trigonometric function?

Inverse trigonometric function is a general term for the functions of arcsine x, arccosine, arctangent x, and arctangent x, which respectively represent the angle of sine weight, cosine, tangent and cotangent x.

But the inverse trigonometric function cannot be a function, because it does not satisfy the one-to-one relationship, it is a one-to-many relationship.

You can draw an image of a trigonometric function with y=x as the symmetry axis, and you can find that it does not satisfy the one-to-one correspondence.

If the inverse trigonometric function is to become a function, the value y of the arcsine function should be limited to -π/2≤y≤π/2, and y should be taken as the principal value of the arcsine function, which is denoted as y = arcsinx. Accordingly, the principal value of the inverse cosine function y=arccos x should be limited to 0 ≤ y ≤π; The principal value of arctangent function y=arctan x is limited to -π/2.

In short, the range of the inverse trigonometric function is an angle, which is more convenient to express.

For example, the angle at which sinx= 1/3 holds. This is not a special angle, but we can express it by an inverse trigonometric function: x=arcsin 1/3.

Solving trigonometric equations is particularly important. However, it should be noted that in general, several loops must be added to the solution set. Because the inverse trigonometric function is a one-to-many relationship.

9. Calculator inverse trigonometric function

Inverse trigonometric function is a basic elementary function. It is the unified weight of functions arcsin x, arccosine arccos x, arctangent arctan x, arccot x, arcsec x and arccsc x, and each function represents the angle of x.

The inverse function of trigonometric function is a multi-valued function, because it does not meet the requirement that the independent variable corresponds to a function value, and its image is symmetrical with its original function about function y = X. Euler put forward the concept of inverse trigonometric function, and expressed it in the form of "arc+function name" for the first time.

(9) Extended reading of anti-trigonometric function network course:

In order to make the interval determined by the single-valued inverse trigonometric function representative, the following conditions are often observed:

1, in order to ensure that the function corresponds to the single value of the independent variable, the determined interval must be monotonous;

2. It is best that the function is continuous in this interval (the reason why it is best here is because the arc tangent and anti-cotangent functions are discontinuous);

3. For the convenience of research, it is often required that the selected interval includes the angle from 0 to π/2;

4. Make sure that the function value domain on the interval should be the same as the definition domain of the whole function. The inverse trigonometric function thus determined is single-valued. In order to distinguish it from the multi-valued inverse trigonometric function above, the notation of a in arc is often changed to a, for example, the single-valued arcsine function is recorded as arcsin X.

10. Please give all the formulas of inverse trigonometric function for self-study.

Arcsinx+Arccosx=π/2，Arctanx+Arccotx=π/2