Rearrange to make they the subject

[laura2988]

Can anyone rearrange the following equation to make theta the subject please ?

A = B * sin(theta) + (B* cos(theta)*C)

Thanks

 

[Otis]

... A = B * sin(theta) + (B* cos(theta)*C)

Hello. Is this equation from a school assignment? We can factor out B and then divide, to write:

A/B = sin(θ) + C ∙ cos(θ)

Solving that equation for θ by hand seems complicated. Without any information about A,B,C, software reports the solution in terms of arctan(y,x) -- a form having two Real inputs y,x which computes the principal value of the argument of the complex number x+i∙y.

Are you sure you've provided all of the given information? Also, please be sure to read the forum's submission guidelines. Thank you.

?

 

[laura2988]

Sorry, I just tried to simplify it. I am trying to work out what the maximum allowable slope would be for a vehicle with four motors in each of the four wheels providing a total torque(T)of 9600Nm, Wheel radius(r) 0.4m, coefficient of friction(u)0.2, vehicle mass(m) 1500kg

Therefore in the equation above I was calculating the forces and was trying to rearrange for theta so I could see what the maximum allowable slope would be before the force exceeded the torque provided by the motors:
A = T/r
B= m*g
C = 0.2

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[Dr.Peterson]

Can anyone rearrange the following equation to make theta the subject please ?

A = B * sin(theta) + (B* cos(theta)*C)

I wonder if you have typed something wrong. Why does the second term have both B and C as coefficients? Does one of your "*"s mean something other than multiplication? Are both B's supposed to be there?

But also, as the guidelines say, please tell us the context of the question, and what you know that might be relevant. It isn't actually that hard to solve, if you know the right identities; but it just doesn't feel right.

 

[MarkFL]

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You appear to be posting a genuine question, so perhaps this spam link was inadvertent, but please make certain your posts do not contain such links in the future, or we will be required to take further action.

 

[Dr.Peterson]

Can anyone rearrange the following equation to make theta the subject please ?

A = B * sin(theta) + (B* cos(theta)*C)

Let's just write it as

[MATH]p\sin(\theta) + q\cos(\theta) = r[/MATH]​

Then if we divide by the appropriate quantity, we get

[MATH]\frac{p}{\sqrt{p^2 + q^2}}\sin(\theta) + \frac{q}{\sqrt{p^2 + q^2}}\cos(\theta) = \frac{r}{\sqrt{p^2 + q^2}}[/MATH]​

which is

[MATH]\sin(\phi)\sin(\theta) + \cos(\phi)\cos(\theta) = \frac{r}{\sqrt{p^2 + q^2}}[/MATH] if we take [MATH]\phi = \tan^{-1}\left(\frac{p}{q}\right)[/MATH].​

Then we have

[MATH]\cos(\theta-\phi) = \frac{r}{\sqrt{p^2 + q^2}}[/MATH]​

and therefore

[MATH]\theta = \phi + \cos^{-1}\left(\frac{r}{\sqrt{p^2 + q^2}}\right)[/MATH]​

Presumably you can apply this to your problem. (I may have missed a case, as I assumed that [MATH]\theta - \phi[/MATH] is in the first quadrant.)

 

[Deleted member 4993]

In addition, we need to assume that:

√(p² + q²) ≥ |r|