- #1
ognik
- 643
- 2
Anyone know a way to calculate x=tan(x)cosh2(x) ? I think I should know - but just blank at the moment.
Not quite. When you truncated the infinite series, you lost some accuracy.ognik said:Sorry, yes, I want to solve x= ½sinh(x). IE 2x = x + x3/3! + x5/5!. Dividing by x gives 2 = 1 + x2/6 + v4/120 + ...
Letting u = x2, I have a quadratic of u2 + 20u - 120 = 0 and the positive root of this is 4.8324, giving x=2.2098 ?
In general, there is no formula for solving polynomial equations of degree 5 and greater. Unless you stumble on some fortuitous factorization, you're basically left with numerical techniques, like iteration or applying Newton's method. Applying things like the Rational Root Theorem and Descartes Rule of Signs may indicate how many real roots exist and which trial values to try, but it's basically trial and error.ognik said:I confess I dropped the x7 and subsequent terms because I don't know how to solve the more complex equation that would result :-( So if I had (say) x8/9! + x6/7! + x4/5! + x3/3! - 1 =0, how would I approach solving that equation without using something like mathematica?
A trigonometric multiplication equation is an equation that involves two or more trigonometric functions being multiplied together, such as sine, cosine, tangent, or their inverse functions.
To solve a trigonometric multiplication equation, you may need to use trigonometric identities, algebraic manipulation, and the unit circle. You may also need to use special angles and reference triangles to simplify the equation.
The steps to solving a trigonometric multiplication equation are as follows:
1. Simplify the equation using trigonometric identities.
2. Use algebraic manipulation to isolate the unknown variable.
3. Use the unit circle or special angles to find the exact value of the trigonometric functions.
4. Check your solution by substituting it back into the original equation.
Some common mistakes when solving trigonometric multiplication equations include:
- Forgetting to use trigonometric identities to simplify the equation.
- Misinterpreting the unit circle or special angles.
- Forgetting to check the solution by substituting it back into the original equation.
- Incorrectly applying algebraic rules, such as distributing or combining like terms.
Yes, you can use a calculator to solve a trigonometric multiplication equation. However, it is important to understand the steps and concepts behind the solution rather than solely relying on a calculator. Additionally, make sure to use the correct mode (degrees or radians) on your calculator for the given problem.