Help with solving for theta

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Summary:

I'm getting some strange answers when I try and solve an equation for theta

Help with solving for theta

Chris (guest) 21 Sep 2014 00:05

Hello,

I'm trying to use my Ti-Nspire CAS to solve a few equations for the variable theta and when I do I get some strange results. I've had this problem before and remember having to enter the equation into the calculator in a certain way, but for the life of me I can't remember what the format was.

Here's what I'm trying to solve. .15*cos(theta) = .26666667 + 9.81*sin(theta) I'm trying to solve for the angle theta and when I enter solve(….) into the calculator it spits out x=6.2831853071796*n1-0.011282597074317 or x=6.2831853071796*n1+3.1846768515479.

I've tried this in radians and degrees, no luck.

How can I get this to just spit out the proper answer, which should be 6.9999?

Thanks for your help.

Chris (guest) 21 Sep 2014 00:08

Forgot one term: .15(9.81)*cos(theta) = .26666667 + 9.81*sin(theta)

Re: Help with solving for theta

Timothy Foster 21 Sep 2014 01:43

Keep in mind that trigonometric functions are periodic. This means that with each period, a new solution will appear, and therefore your equation has infinitely many solutions. The calculator's answer encodes all of those solutions. The solution $x = a*n + b$ says that for each integer value of $n$, a solution $x$ exists that follows the given equation.

Interestingly, the calculator is actually giving you the answer you want. In your modified equation, the answer would be 6.2831853071796*n1-2.96582 or 6.2831853071796*n1+0.122004. If we choose n1 to be 0, then we get that x is either -2.96582 or 0.122004 radians. The positive one, 0.122004, is equal to 6.9903 degrees.

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Timothy Foster - @tfAuroratide
Auroratide.com - Go here if you're nerdy like me

Chris (guest) 21 Sep 2014 14:52

Wow, I had no idea it was that easy. Thank you for explaining this to me. Now I suppose the difficult task is up to me on deciding which solution is realistic. In the problem above we we're optimizing theta such that a box on a conveyer belt doesn't slip. Taking the two solutions (when n1 = 0 and 1) the corresponding angles are 6.9903 and 190.071. Clearly with a little intuition 190 degrees can't be true.

Thanks again for the help, I really appreciate it.