Equation with inverse cosine needed to be rewritten

In summary, the conversation discusses a request for help in rewriting an equation as a function of y and whether it is possible to get y out of the equation. The purpose of this is to calculate the liquid height in an LPG tank. It is suggested that it may not be possible to do so algebraically and a reference to Kepler's equation is provided.
  • #1
-bLazE-
1
0

Homework Statement


I need to rewrite this equation as a function of y. would love some help since i failed on the right side of the equation.

v= [πr(3R-y)y²]/3R + L√[(2R-y)y(y-R)+R²cos^-1(1- y/R)]

i mean is it even possible to get y out of there, with inverse cosine and all?
Thanks in advance.


@gabbagabbahey
there isn't any original question. i wanted to get this equation in order to use in calculating the liquid height in an LPG tank. The equation above gives the liquid volume in the tank as long as you have the liquid height. i want to make use of it in reverse. i have the liquid volume and want to calculate the liquid height.
 
Last edited:
Physics news on Phys.org
  • #2
What was the original question?
 
  • #3

FAQ: Equation with inverse cosine needed to be rewritten

1. What is an equation with inverse cosine?

An equation with inverse cosine contains the inverse of the cosine function, which is denoted as cos^-1 or arccos. This function is used to find the angle whose cosine is equal to a given value.

2. Why would an equation with inverse cosine need to be rewritten?

An equation with inverse cosine may need to be rewritten if it is in a form that is difficult to solve or if the given value is not in the range of the inverse cosine function. Rewriting the equation can make it easier to solve and provide a more accurate answer.

3. How do you rewrite an equation with inverse cosine?

To rewrite an equation with inverse cosine, you can use the trigonometric identity cos^-1(x) = π/2 - sin^-1(x). This identity can be applied to simplify the equation and make it easier to solve.

4. Can an equation with inverse cosine have multiple solutions?

Yes, an equation with inverse cosine can have multiple solutions. This is because the cosine function is periodic and has values that repeat every 2π. Therefore, the inverse cosine function can have multiple solutions within a given range.

5. Are there any common mistakes when solving an equation with inverse cosine?

One common mistake when solving an equation with inverse cosine is forgetting to check the range of the inverse cosine function. The inverse cosine function only has values between -1 and 1, so if the given value is outside of this range, the equation may not have a solution. It is important to always check the range and adjust the equation if necessary.

Similar threads

Direction in which directional derivative is zero
Replies
6
Views
1K
Finding the Centre of Mass of a Hemisphere
Replies
9
Views
1K
Rate at which a bucket gets filled
Replies
4
Views
2K
Finding the parametric equation of a curve
Replies
2
Views
2K
Work problem -- lifting water out of tanks
Replies
2
Views
2K
Avoid unpleasant integrals in solving IVP
Replies
3
Views
1K
Deriving a volume formula, answer seems to be correct but is negative.
Replies
6
Views
2K
How Do You Find the Inverse Laplace Transform for a Given Differential Equation?
Replies
6
Views
1K
Singularities when applying Stokes' theorem
Replies
2
Views
1K
ODE homogeneous equations w/constant coefficients
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top