Thread: Need help solving trig Equation

1. Need help solving trig Equation

Hey, I am currently trying to solve some maths equations, and cannot seem to think of how to solve this trig equation:

$k1*sin(2*theta) + k2*cos(theta + k3) = k4$

Where k1,k2,k3,k4 are all constants and I would like to solve for theta.

I would appreciate any help given, thanks!

2. Heres another equation I have come up with that I would like to solve:

$k1*sin^2(theta) + k2*2*(sin(theta)*cos(theta)) +$
$k3*cos^2(theta) + k4*cos(theta) + k5*sin(theta) = k6$

Where k1,k2,k3,k4,k5,k6 are constants and would like to solve for theta.

Im trying to solve this so that I can use it in a program I am making, it is generated from a set of equations im trying to solve which can be solved using the quartic euqation but I would prefer a solution which involves less operators used .

Thanks again.

3. Originally Posted by FireSoul
Hey, I am currently trying to solve some maths equations, and cannot seem to think of how to solve this trig equation:

$k1*sin(2*theta) + k2*cos(theta + k3) = k4$

Where k1,k2,k3,k4 are all constants and I would like to solve for theta.

I would appreciate any help given, thanks!
You may be somewhat out of luck. This sort of thing does not submit to full, complete, or closed-form solution. If you're lucky, you may be able to find parameters that will provide a nice solution. Generally, though, after picking the 'k's, you are most likely stuck with numeric solutions. Even this is a tenuous process, as these are periodic functions and you need to make up your mind exactly which solutions you want. On the other hand, none of your parameters changes the period, os at least it's predictable.

For k1 = k2 = k3 = k4 = 1, I get solutions $\theta = 4.599$ and $\theta = 3.765$. Again, that's just two of the infinitely many solutions.

Where does all that leave us?