Solving an equation containing sine and cosine

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.

Answer 1

[Matt Fig]

If you have the symbolic toolbox, use SOLVE:

solve('A*cos(x)+B/sin(x)=C','x')

[Hamish]

Yes, of course. Thank you so much. I knew this earlier but somehow completely forgot about it and was frustrating.

Answer 2

[Babak]

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

Answer 3

[Manal Alhammadi]

where y=2+3e^(-2t) t=0:0.1:3

Answer 4

[Manal Alhammadi]

y=2+3e^(-2t)

Answer 5

[Cheng Chen]