Solving an equation containing sine and cosine
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This might sound silly, so please be patient. I am not a complete beginner at Matlab but I seem to be stuck with this small problem: How do I solve for x? The equation is
A*cos(x)+B/sin(x)=C where A,B and C are constants
Thanks in advance.
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Babak
2012-8-14
A*cos(x)+B/sin(x)=C
multiply both sides by sin(x) to get:
A * sin(x)*cos(x) + B = C * sin(x)
now use the following relations: sin(x) = 2u/(1+u^2) and cos(x)=(1-u^2)/(1+u^2) where u=tan(x/2) to get:
A*(2*u)*(1-u^2)+B(1+u^2)^2=C*(1+u^2)*2u
which is a fourth order equations. I would simplify it and solve it numerically with fsolve:
B*u^4-2*(A+C)*u^3+2*B*u^2+2*(A-C)*u+B=0
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