# Solving trigonometric equation

• Nopollution
In summary, a trigonometric equation is an equation that involves trigonometric functions and is typically used to solve for unknown angles or sides in a triangle. To solve these equations, algebraic methods and trigonometric identities and properties are used. Some common identities and properties include the Pythagorean identities, sum and difference formulas, double angle formulas, and half angle formulas. To check the correctness of a solution, one can plug in the values found for the unknown variables and use a calculator or graphing software. Tips for solving trigonometric equations include rewriting the equation in terms of one trigonometric function and being familiar with basic identities and properties.
Nopollution
Hi guys,

I need to solve the following trigonometric equation. Some time ago I would have used Fortran with the appropriate libraries but now I was wondering whether there is any better approach. Any suggestion?

w^2/c^2= k//^2 - Sqrt(w^2 Eps_b^2/c^2 - k//^2) * Tan[Sqrt(w^2 Eps_b^2/c^2 - k//^2) * d/2]

where:
c= speed of light in vacuum
k//= variable
d= parameter
w= frequency
Eps_b= parameter

I need to plot w(k//) keeping in mind that "c", "d" and "Eps_b" are just parameters.

Cheers

Use an online tool for a numeric solution.

## 1. What is a trigonometric equation?

A trigonometric equation is an equation that involves one or more trigonometric functions, such as sine, cosine, tangent, etc. These equations are typically solved to find the values of the unknown angles or sides in a triangle.

## 2. How do I solve a trigonometric equation?

To solve a trigonometric equation, you need to use algebraic methods to isolate the trigonometric function on one side of the equation. Then, you can use trigonometric identities and properties to simplify the equation and find the values of the unknown variables.

## 3. What are some common trigonometric identities and properties?

Some common trigonometric identities and properties include the Pythagorean identities, sum and difference formulas, double angle formulas, and half angle formulas. These identities and properties are useful for simplifying trigonometric equations and solving for unknown variables.

## 4. How do I know if my solution to a trigonometric equation is correct?

You can check your solution by plugging in the values you found for the unknown variables into the original equation. If the equation is true, then your solution is correct. Additionally, you can use a calculator or graphing software to verify your solution.

## 5. Are there any tips for solving trigonometric equations?

One helpful tip for solving trigonometric equations is to try to rewrite the equation in terms of one trigonometric function. This can make the equation easier to work with and can reveal any hidden identities or relationships. It is also important to be familiar with the basic trigonometric identities and properties, as they can be useful in simplifying equations. Practice and patience are key when solving trigonometric equations.

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