Solve Equation numerically for variable

2016 7 21
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更新时间：2016 7 21
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Need to solve this problem for w:
0 = A + Bcos(w) + Ccos(w) ( A,B,C Constants)
Bounds should be 0-180 for this problem I believe, two solutions possible?

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回答（2 个）

Azzi Abdelmalek
Azzi Abdelmalek 2016-7-21

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solve('A + B*cos(w) + C*cos(w)')

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Philip Hoskinson
Philip Hoskinson 2016-7-21
The following error occurred converting from sym to double: Error using symengine (line 59) DOUBLE cannot convert the input expression into a double array. If the input expression contains a symbolic variable, use VPA.
Error in Post_Final (line 40) HourAngleSunrise_Degrees(i) = rad2deg* solve('A + B*cos(w)+C*sin(w)')
A, B, C are values calculated from matrixes, so A = sin(matrix(i)) etc
Philip Hoskinson
Philip Hoskinson 2016-7-21
Original question had an error that makes this more complicated: Actual equation:
0 = A + Bcos(w) + *Csin(w)*
or with identity:
0 = A = Bcos(w) + Csqrt(1-cos^2(w))

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Star Strider
Star Strider 2016-7-21

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If ‘A’, ‘B’ and ‘C’ are matrices, then:
w = acos(-(B+C)\A);
assuming that the matrices have the appropriate dimensions, and the resulting argument matrix ‘(-(B+C)\A)’ elements are all between -1 and +1.

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Philip Hoskinson
Philip Hoskinson 2016-7-21
Original question had an error that makes this more complicated: Actual equation:
0 = A + Bcos(w) + *Csin(w)*
or with identity:
0 = A = Bcos(w) + Csqrt(1-cos^2(w))
Star Strider
Star Strider 2016-7-21
The Symbolic Math Toolbox comes up with these solutions for ‘w’ that would also work for matrices:
syms A B C w
w_sol = solve(A == B*cos(w) + C*sin(w), w);
w_sol = simplify(w_sol, 'steps',10)
-log((A + (A^2 - B^2 - C^2)^(1/2))/(B - C*1i))*1i
-log((A - (A^2 - B^2 - C^2)^(1/2))/(B - C*1i))*1i
Use the sqrtm and logm functions. Also see the funm function. If you know that your matrices will always be real or positive, you can tell the Symbolic Math Toolbox to assume that. It may simplify the result.

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