What would you do if you need to find a relation between two variables but the one that you need to find in function of the other is the argument of a tangent ($\tan(y)$) ? For example if I have the equation: $$x= K+y\tan(\sqrt{y})+y$$ How do you find the $y$ in function of $x$? I need it to determine a dispersion relation and I want to avoid graphical solutions.
2026-04-01 04:54:59.1775019299
Solve an equation in which a variable is an argument of a tangent: $x= K+y\tan(\sqrt{y})+y$
86 Views Asked by Simon https://math.techqa.club/user/simon/detail At
1
There are 1 best solutions below
Related Questions in TRIGONOMETRY
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- Finding the value of cot 142.5°
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Sine of the sum of two solutions of $a\cos\theta + b \sin\theta = c$
- Tan of difference of two angles given as sum of sines and cosines
- Limit of $\sqrt x \sin(1/x)$ where $x$ approaches positive infinity
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Why are extraneous solutions created here?
- I cannot solve this simple looking trigonometric question
Related Questions in CLOSED-FORM
- How can I sum the series $e^{-2}\frac{(3)^n}{n!}\sum_{k=0}^{\infty}\left ( \frac{1}{2}\right )^k\frac{1}{(k-n)!}$
- Computing $\int_0^\pi \frac{dx}{1+a^2\cos^2(x)}$
- Can one solve $ \int_{0}^\infty\frac{\sin(xb)}{x^2+a^2}dx $ using contour integration?
- Finding a closed form for a simple product
- For what value(s) of $a$ does the inequality $\prod_{i=0}^{a}(n-i) \geq a^{a+1}$ hold?
- Convergence of $\ln\frac{x}{\ln\frac{x}{\ln x...}}$
- How can one show that $\int_{0}^{1}{x\ln{x}\ln(1-x^2)\over \sqrt{1-x^2}}\mathrm dx=4-{\pi^2\over 4}-\ln{4}?$
- Exercises about closed form formula of recursive sequence.
- Simplify and determine a closed form for a nested summation
- Direction in closed form of recurrence relation
Related Questions in INVERSE-FUNCTION
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Combination of functions and their inverses.
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
- Find the greatest and least values of $(\sin^{-1}x)^2+(\cos^{-1}x)^2$
- Is it always possible to rearrange an equation desirably?
- Only bijective mappings are invertible. Clarifying proof.
- Relating the roots of quadratic to an inverse trigonometric functions' question
- Derive the conditions for $\tan^{-1}\frac{a\cos x-b\sin x}{b\cos x+a\sin x}=\tan^{-1}\frac{a}{b}-x$
- Why is the inverse of the derivative of f not the actual derivative of the inverse of f?
- $\ {\sin}^{-1}{(x)} $ equation and function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
When you give an implicit function definition, finding y=f(x) explicitly is not guaranteed (and oftentimes impossible).
What you could do could be to solve numerically, that is, loop for x in a certain range and search for an approximate solution s.t. x-h(x,y) ~ 0. You can use any root finding algorithm that you would like, Newton, bisection ...