Solving Equation from "Belt Problem": Find Alpha

  • Thread starter itchy8me
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In summary, the person is asking for help with an equation they derived from a "belt problem" and are trying to solve for alpha. However, with alpha both inside and outside a transcendental function, a numerical solution may be the best option. They also mention that there are infinitely many solutions due to the periodic nature of cos. They thank the person who provided help and mention that graphing may also be a possible solution method.
  • #1
itchy8me
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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:

[tex]\frac{1}{\alpha}[/tex] * [tex]\left(\frac{4}{cos(\alpha)} + 9,5\right)[/tex] = [tex]\frac{1}{36}[/tex]

anybody know the direction i should take to solve this?

thanks,
wernher
 
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  • #2
With the "unknown", [itex]\alpha[/itex] 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.
 
  • #3
may i ask what is that comma in the equation?
 
  • #4
darkmagic said:
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.
 
  • #5
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.
 
  • #6
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.
 

1. What is the "belt problem"?

The "belt problem" is a mathematical problem that involves finding the unknown angle (alpha) in a right triangle, given the lengths of the two sides of the triangle and the radius of a circle inscribed within the triangle.

2. Why is it important to solve equations from the "belt problem"?

Solving equations from the "belt problem" can help us understand and solve similar mathematical problems in real-life situations, such as calculating the angle of a roof or determining the optimal angle for a ramp.

3. How do you solve equations from the "belt problem"?

To solve equations from the "belt problem", you can use the trigonometric functions sine, cosine, and tangent. The specific function to use depends on the given information and which side of the triangle you are trying to solve for.

4. What is the purpose of finding alpha in the "belt problem"?

The purpose of finding alpha in the "belt problem" is to determine the angle of the triangle, which can be used to solve various real-life problems involving right triangles.

5. What are some tips for solving equations from the "belt problem"?

Some tips for solving equations from the "belt problem" include drawing a diagram to visualize the problem, using the Pythagorean theorem to find missing side lengths, and double-checking your calculations to ensure accuracy.

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