Solving -25FCosα + 1.5FSinα= -80 with Trigonometric Identities

[Esas Shakeel]

-25FCosα + 1.5FSinα= -80

Can someone please solve this and tell what trigonometric identities are we going to be using this solving?

 

[blue_leaf77]

There are two unknowns in one equation, doesn't seem to be solvable.

 

[SteamKing]

-25FCosα + 1.5FSinα= -80

Can someone please solve this and tell what trigonometric identities are we going to be using this solving?

I can't think of any. For a given value of F, your best bet would be to iterate to find the angle α which satisfies this equation.

 

[Ssnow]

You can try with some methods for solving trigonometric equations... For example putting $X=\cos{\alpha}$ and $Y=\sin{\alpha}$ you can form the system $\left\{ \begin{array}{rl} -25FX+1.5FY=-80 \\ X^2+Y^2=1 \end{array} \right.$

 

[Esas Shakeel]

Im so sorry i forgot to mention the value for F! Its 4kN
@Ssnow @SteamKing

 

[Samy_A]

In general, an equation $a\sin(\alpha) + b\cos(\alpha)=c$ can be rewritten as
$sin(\alpha + \beta)=\frac{c}{\sqrt{a²+b²}}$,
where $\beta$ satisfies $\cos(\beta)=\frac{a}{\sqrt{a²+b²}}$, $\sin(\beta)=\frac{b}{\sqrt{a²+b²}}$.

 

[blue_leaf77]

You can try with some methods for solving trigonometric equations... For example putting $X=\cos{\alpha}$ and $Y=\sin{\alpha}$ you can form the system $\left\{ \begin{array}{rl} -25FX+1.5FY=-80 \\ X^2+Y^2=1 \end{array} \right.$

That still gives three unknowns with two equations.

 

[SteamKing]

That still gives three unknowns with two equations.

But F = 4 kN, according to the OP. It's still not clear if 80 is in kN or what.

Knowing a value for F, you can still solve the original equation by iterating for the angle α.

-100 kN ⋅ cos α + 6 kN ⋅ sin α = -80 kN (?)

f(α) = 80 - 100 ⋅ cos α + 6 ⋅ sin α

   α         f(α)
  Deg.       kN
  10       -17.44
  15       -15.04
  20       -11.92
  25        -8.10
  30        -3.60
  35        +1.53

α lies somewhere between 30° and 35°.

You can continue the iteration to reach the desired precision for α.

 

[Ssnow]

Yes @blue_leaf77, it will be a system with three unknowns and two equations, or a system with two unknowns, one parameter $F$ and two equations :-D