![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Inverse trigonometric function table Inverse trigonometric function table It's the sine, cosine, tangent value corresponding to each angle value It's better to show how to find inverse trigonometric functions by hand
arcsin0 = 0,
arcsin (1/2) = π/6,
arcsin(√2/2) = π/4,
arcsin(√3/2) = π/3,
arcsin 1 = π/2
atccos1 = 0,
arccos (√3/2) = π/6,
arccos (√2/2) = π/4,
arccos (1/2) = π/3,
arccos 0 = π/2
arctan0 = 0,
arctan (√3/3) = π/6,
arctan (1) = π/4,
arctan (√3) = π/3,
arctan 0 = π/2
Inverse trigonometric function table
You can use the calculator that comes with windows
Start - program - Accessories - Calculator - check - Scientific - Inv - input function value - point corresponding trigonometric function symbol
Inverse trigonometric function: arctg (- 238.06162) / 213.8381 =?
0.41975 ° 0.007326 rad
Inverse trigonometric function equation arctg (x) + arctg (3x) = 90 ° give a rough algorithm on the line
If a = arctg (x), then 90 ° - a = arctg (3x)
Then x = Tan (a), 3x = Tan (90 ° - a) = cot (a)
So 3x = 1
X = √ 3 △ 3 (negative value is not allowed)
Arctg (0.1 / 0.75) = 7.576 degrees, then - arctg (0.1 / 0.75) =?
If arctg (0.1 / 0.75) = 7.576 degrees, - arctg (0.1 / 0.75) = - 7.576 degrees or (180-7.576) = 172.424 degrees
Proof of determinant of linear algebra prove 1+a1 1 1 ...1 1 1+a2 1 ...1 1 1 1+a3 ...1 . 1 1 1 ...1+an =A1A2... An (1 + 1 / AI)
Classic old topic
I'll write some steps and I'll see them
(1) Starting from the second line, each row subtracts the first line
1+a1 1 1 ...1
-a1 a2 0 ...0
-a1 0 a3 ...0
.
-a1 0 0 ...an
(2) The second line is divided by A2, the third line is divided by A3... And the nth line is divided by an
1+a1 1 1 ...1
-a1/a2 1 0 ...0
-a1/a3 0 1 ...0
.
-a1/an 0 0 ...1
*(a2a3...an)
(3) Subtract the following lines from the first line
M 0 0 ...0
-a1/a2 1 0 ...0
-a1/a3 0 1 ...0
.
-a1/an 0 0 ...1
*（a2a3...an）
The M position is: (1 + A1) + A1 / A2 + A1 / A3 +... + A1 / an
(4) Original formula = m * (a2a3... An)
=A1A2... An (1 + 1 / AI)
The proof of linear algebra uses the definition of determinant to prove that if there are more than n ^ 2-N elements of an n-order determinant as 0, then the determinant is 0
According to the drawer principle, at least one line of elements is 0
Determinant definition is the accumulation of all elements of different rows and columns
If a row is all 0, then each of the above items is 0, so the determinant is 0
It's a property, but it's only a step further than the definition. You just don't use the property directly
How to prove the property 6 of determinant in Tongji version of linear algebra
Divide the determinant of 5 into two determinants
One of them is equal to the original determinant, and the other is proportional to 0
Determinant property 5 how to prove, Tongji version of linear algebra
Double click to see a larger picture
In engineering mathematics linear algebra Tongji fifth edition P10 property 2 two rows (columns) of commutative determinant, determinant change sign. The proof process is a little incomprehensible Set determinant It is obtained by the determinant d = det (AIJ) replacing the two rows I and j, that is, if When k ≠ I, J, BKP = AKP; when k = I, J, BiP = AJP, BJP = AIP D1= ∑(-1)tb1p1… bipi… bjpj… bnpn = ∑(-1)taip1… ajpi… aipj… anpn = ∑(-1)ta1p1… aipj… ajpi… anpn Among them, 1 i… j… N is natural permutation, t is permutation P1 pi… P J ... Let the permutation P1 pj… pi… The reverse order number of PN is Then (- 1) t = - (- 1) T1 Dj= -∑(-1)t1a1p1… aipj… ajpi… anpn= -D The above is the complete proof process on the book The other parts are very clear, of which I don't understand the most Does it mean that in the latter step, DJ = - D = - 1 t1a1p1… aipj… ajpi… Anpn? However, D is the newline (column) The previous determinant is not supposed to be D=∑(-1)ta1p1… aipi… ajpj… Anpn? Unless I have a problem with my thinking. Then if I have a problem with my thinking How is the equation of the last step derived What about it? I don't have a good math foundation. I want to do well Understand the knowledge in the textbook
You are the same as I thought before. Now I have understood. To understand this step, you have to be very clear about the definition of the expression of determinant. Determinant is the algebraic sum of n! Terms. Each term is the product of N numbers in different columns in different rows, plus the t power of sign (- 1). The key is how to get t, which is how to get every
RELATED INFORMATIONS
- 1. Both a and B are orthogonal matrices. The determinant of a + B = 0. It is proved that the determinant of (a + b) is equal to 0
- 2. How to express the present value, final value coefficient, (formula), (what do P / A, P / F mean), calculation formula, how to calculate
- 3. Mathematical formula and definition of grade one to grade six in primary school (PEP)
- 4. Please fill in the number represented by X to make the equation true (1） X÷X=X2 X=（ ） （2）X+X=2X X=( ) (3) X2=2X X=( ) (4) X2=X-X X=( ) Which prawn can help me to solve it!
- 5. 11 + 1 + 1 - 111 = 4 move a matchstick to make the equation hold!
- 6. It is proved by mathematical induction that the nth power of 2 > 2n + 1 (n ∈ n *, n ≥ 3)
- 7. Mathematical induction to prove inequality (1 / N + 1) + (1 / N + 2) +. + (1 / 3N + 1) > 25 / 24
- 8. Given that a, B and C are the three sides of the triangle ABC, and a square C square - b square C square = a 4 power - B power, try to judge the shape of the triangle ABC
- 9. Given that a, B, C are the three sides of the triangle ABC and satisfy the relation a ^ 2 + C ^ 2 = 2Ab + 2bc-2b ^ 2, try to judge the shape of the triangle ABC and explain your reasons
- 10. It is known that a, B and C are the three sides of a triangle, a = 2n 2 + 2n, B = 2n + 1, C = 2n 2 + 2n + 1 (n is a natural number greater than 1), we try to explain that △ ABC is a right triangle
- 11. Ask a question, very urgent Oh/ If the function y = (m-2) x ^ (m ^ 2-m-3) is an inverse proportional function of X 1. Find the value of M 2. Write the analytic trial and the proportional coefficient of the function
- 12. A three digit number is equal to 19 times the sum of its digits. What is the sum of the largest and the smallest of the three digits?
- 13. For 3 - 1 - 4 three numbers, the following operations are carried out: take two arbitrary numbers, divide their sum by root 2, their difference is also divided by root 2, add a number that was not taken before, and then generate three numbers. Can the sum of squares of three numbers be equal to 2008 after repeating the above operation several times?
- 14. Calculus inverse function Y = 2 sin (3x) times to find the inverse function, I can not find X I can only work out sin (3x) = LN2 divided by LNY, and then I won't. and how to do this kind of problem is equivalent to y = 1 + ln (x + 2)
- 15. What is the inverse function to the power of X + 1 of function y = 2? Well, I got it down to log2 (y) = x + 1, x=log2（y）—1=log2（y）—log2（2）=log2（y/2） That's all I can do
- 16. High inverse function, There is no inverse function for the power function y = x ^ 2. Why? Detailed explanation, thank you If the power function y = x ^ a (a > 0) has an inverse function, then a can take____ If the power function y = x ^ a (a)
- 17. The known function f (x2 − 3) = lgx2 x2−6． (1) The definition domain of function f (x) is obtained; (2) the parity of function f (x) is judged; (3) Find the inverse function of F (x); (4) if f [φ (x)] = lgx, find the value of φ (3)
- 18. Given that the inverse function of the function f (x) = 3x passes through the point (18, a + 2), let the definition domain of G (x) = 3ax-4x be the interval [- 1,1], and obtain the analytic expression of G (x); 3x: 3 to the power of X, 3ax: 3 to the power of ax, 4x: 4 to the power of X
- 19. Can the definition domain of y = (1-x) / (1 + x) take 0? The value range of its inverse function cannot be - 1, so the definition field should not take 0, right?
- 20. Find the inverse function y = x / (x + 2)