# Solving an equation containing sine and cosine

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Hamish on 14 Aug 2012
Answered: Cheng Chen on 26 Sep 2020
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

Matt Fig on 14 Aug 2012
If you have the symbolic toolbox, use SOLVE:
solve('A*cos(x)+B/sin(x)=C','x')
Hamish on 14 Aug 2012
Yes, of course. Thank you so much. I knew this earlier but somehow completely forgot about it and was frustrating.

Babak on 14 Aug 2012
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

Manal Alhammadi on 31 Jan 2018
where y=2+3e^(-2t) t=0:0.1:3

Manal Alhammadi on 31 Jan 2018
y=2+3e^(-2t)

Cheng Chen on 26 Sep 2020 