Solve

Question

Hi.
How can i solve for the angle and get it into a number not a matrix?

Werner_E · Accepted Answer

@kenan2 wrote:I don't understand how the equation can have different solutions when in the solution manuel is the answer: 53.1 deg.The pure mathematical problem you posed first (the equation with trig functions) has an infinity number of solutions. But for your application I'd guess that only solutions in the range 0° to 90° (or 0 to pi/2) are physically relevant. So you have to tell Mathcad that you are only interested in solutions within that range. Trivially theta=0 is a "solution" to your problem, too, as Luc has explained, but sure not the solution you had in mind. Then is seems you gave a wrong equation in your very first post with a superfluous factor 2. This equation would give you an angle of 69.44 °.The equations you posted later seems to be the correct one.So use this second equation, tell Mathcad via assumptions that you only are interested in solution within the aforementioned range and let Mathcad show the result in degree rather than the default radian and you get what you are looking for.

Werner_E · Answer

Don't only post a picture - additionally post you worksheet as it makes it easier for us to play around with and show you with your exact example what we are talking about.

@kenan2 wrote:

Hi.

How can i solve for the angle and get it into a number not a matrix?

Your solution ARE numbers, but as there are more than one, Prime combines them in a vector.

Your equations has an infinite number of solutions. Mathcad shows you the three within the range [-pi; pi].

How should Prime know which of the solutions is the one you need if you don't tell it?

1) You may assign the outcome of the symbolic solve to a variable -> sol:=.... and then access the solution which is suitable for your application via vector index, e.g. theta := sol[2

2) You may use the assume modifier to only get the solution you are looking for, maybe like "assume, -pi<theta<-pi/2"

3) You may use a numeric solve block instead of the symbolic solve. Here you can apply additional constraints (like theta<0 or the like) and also control the outcome by using different guess values.

BTW, its expected of you that you come back to a question you asked and close the thread (e.g. by marking an answer as being correct or by assuming the question to be answered. And its not wrong to let people know if their answer had helped.

-> https://community.ptc.com/t5/PTC-Mathcad-Questions/Isolate/m-p/552340

-> https://community.ptc.com/t5/PTC-Mathcad-Questions/massflow-rate/m-p/549645