Equation of trigonometric function Given that 3sin? α + 2Sin? β = 2Sin α, find the value range of sin? α + sin? β

Equation of trigonometric function Given that 3sin? α + 2Sin? β = 2Sin α, find the value range of sin? α + sin? β

From 3 sin 2 α + 2 sin 2 β = 2 sin α
2 sin 2 β = 2 sin α - 3 sin 2 α
Because 0 ≤ sin ^ β ≤ 1
0 ≤ 2 sin α - 3 sin 2 α ≤ 2
The solution is: 0 ≤ sin α ≤ 2 / 3
y=sin²α+sin²β=-1/2sin²α+sinα=-1/2(sinα-1)²+1/2
Sin α = 0, the function value y is minimum 0
Sin α = 2 / 3, function value y Max 4 / 9

Mathematical solution of trigonometric function equation sin2x=-cos(7π/2) The answer is x = 5 π / 8 7 π / 8 11 π / 8 15 π / 8 What is the answer process? The answer is wrong. The third is 13 π / 8 --.

The correct title should be sin2x = - cos (7 π / 4) sin2x = - cos (7 π / 4) = - cos (3 π / 4) = - √ 2 / 2 case 1: 2x = 5 π / 4 + 2K π x = 5 π / 8 + K π (k belongs to integer) case 2: 2x = 7 π / 4 + 2K π x = 7 π / 8 + K π (k belongs to integer) there are infinite solutions

How to solve the equations of trigonometric function by Matlab is as follows

A1, A2, B1, B2, C1, C2 are constants, which can be completely included by a, B, C. for example:
1.solve('1=2-x*tan(3*y)','x')
ans =
1/tan(3*y)
2.solve('1=2-x*tan(3*y)','y')
ans =
1/3*atan(1/x)

Solving equations in MATLAB syms x y z t [x,y,z,t]=solve(2*x+3*y-z+t-2,5*x+y+z-t-13,x-y+2*z+2*t-3,3*x+2*y+2*z+9*t+3) Results: X= -2 Y = One Z = Two T = Four The result is not correct syms x y z t [t,x,y,z]=solve(2*x+3*y-z+t-2,5*x+y+z-t-13,x-y+2*z+2*t-3,3*x+2*y+2*z+9*t+3) result: T = -2 X = One Y = Two Z = Four This is correct Why is this? Thank you for your answer. However, since you said that, I would like to know how to determine the position of the unknown number? Is it in alphabetical order? Can rocwoods answer again. I have raised the score to 30

If you do not know the sequence of [x 2, X 4-2, y + T + 2, y + T + 2, y + T + 2, y + T + 2, y + 2, y + 2, x, x, x, y, x, x, y, x, y, x, y, x, y, x, y, x, y, x, y, x, x, y, x, y, x, x, x, y, x, x, y, x, x, x, y, x, x, x, x, y, X, x, x, x, x, x, y, x, x, x, x, y + X, y + 2, x, x, y + 2, x, x, y + 2, x, y + 2, x, x, y + 2, x, y + X, y + X
T stores T, X stores x, y stores y, Z stores Z, of course, the same as the actual results
However, if [x, y, Z, t] = solve (2 * x + 3 * Y-Z + t-2,5 * x + y + z-t-13, X-Y + 2 * Z + 2 * T-3, 3 * x + 2 * y + 2 * Z + 9 * t + 3), then x is actually stored in T, y is stored in X and so on
The following is the help information in Matlab:
For a system of equations and an equal number of outputs,the results are sorted alphabetically and assigned to the outputs.
"Alphabetically" means alphabetic

How to solve equations with MATLAB syms A B P [A,B,P]= solve(12.56*(A-311)=-20.9*(B-311),B/311=P^0.71,933*P=A*20+B) It turned out to be wrong [A,B,P]=solve(12.56*(A-311)=-20.9*(B-311),B/311=P^0.71,933*P=A*20+B) Error:The expression to the left of the equals sign is not a valid target for an assignment.

Charizing Operator
>> [A,B,P]= solve('12.56*(A-311)=-20.9*(B-311)','B/311=P^0.71','933*P=A*20+B')
A =
58.505380691632510208368024800025
B =
462.73839323029165893698074681874
P =
1.7501029014608165735309123717248

Solving equations with MATLAB How to use matlab to solve bivariate linear equations? For example, y = 2x + 3 y=3x-7 How to use matlab to achieve it?

1、 Two symbolic variables are defined by using the solve function > > Syms x y;% in MATLAB; > > [x, y] = solve ('y = 2 * x + 3 ','y = 3 * X-7');% to define a 2x1 array to store x, Y > > x > > x = 10.0000 > > y > > y = 23.0000 2

Solving trigonometric function equation with MATLAB cos（0.5*x）*cosh（0.5*x）=-1 There should be many x values satisfying the condition. Solve two of them

You can use the fsolve command, which can solve the solution near a certain x value, that is, f (x) = 0
The details are as follows
It's near six
[x,fval]=fsolve(@(x)cos(0.5*x)*cosh(0.5*x)+1,6)
X =
three point seven five zero two
fval =
-1.3868e-007
It's near 9
[x,fval]=fsolve(@(x)cos(0.5*x)*cosh(0.5*x)+1,9)
X =
nine point three eight eight two
fval =
2.4299e-009

Ask the basic question of point trigonometric function Well, the passers-by's help, in your words The relationship between sin cos Tan cots and what do they represent I've learned to say... But I haven't opened my book for a long time Don't encyclopedia. What I read is still a little boring Oh, and arccos arcsin arctan arccot

If sin is a sine function, cos is a cosine function, Tan is a tangent function, cot is a cotangent function. If SiNx = a, cosx = B, TaNx = C, Cotx = D, then a * a + b * b = 1CD = 1A / b = CB / a = darcina = xarccosb = xarctanc = xarccotd = x and sinhx = [e ^ x +...]

Mathematical inverse trigonometric function! Why is the scope of value domain definition?

First of all, you must be clear that the condition for the existence of inverse function is that the original function is continuous and monotonous. Second, when the anti trigonometric function was invented, it was stipulated by the first person, and then it was established by convention

On mathematical inverse trigonometric functions For example, sin (A / 2 + x) = B, where a and B are constants, the value of X should be x = arcsin (b) - A / 2, Then, if arcsin (A / 2 + x) = B, is x = sin (b) - A / 2,

Yes, that's right. Arcsin (a) = B is equivalent to SINB = a