Solving Equation from "Belt Problem": Find Alpha

[itchy8me]

hi there. I have an equation i derived from a "belt problem" (i actually don't know if it's correctly derived yet). However i am now stuck and cannot find the next step to solving it, I'm trying to solve for alpha. The equation is:

$$\frac{1}{\alpha}$$ * $$\left(\frac{4}{cos(\alpha)} + 9,5\right)$$ = $$\frac{1}{36}$$

anybody know the direction i should take to solve this?

thanks,
wernher

 

[HallsofIvy]

With the "unknown", $\alpha$ both inside and outside a transcendental function, you aren't going to be able to find an exact, algebraic, solution. Your best bet is probably a numerical solution.

 

[darkmagic]

may i ask what is that comma in the equation?

 

[rasmhop]

may i ask what is that comma in the equation?

The equivalent of . (dot). In some countries the notation 9,5 is used instead of 9.5 (I know this to be the case in several European countries).


As far as the original equation goes you're not going to find a nice solution to it as HassofIvy mentioned. In fact due to the periodic nature of cos there are infinitely many solutions to the equation.

 

[itchy8me]

mmm.. i guess i'll have to go at the problem another way. thanks for the help, i probably would have stared at this for hours before moving on.

 

[Live2Learn]

You could also solve it graphically. First simplify the equation to:

sec(α) = (1/144)α - 2.375

Then graph y₁=sec(α) and the line y₂=(1/144)α – 2.375

The points of intersection are solutions.