That's a bit complicated but you could do this: Let y= cos(X). Since [itex]sin(x)= \sqrt{1- cos^2(x)}[/itex] we have [itex]2= 3\sqrt{1- y^2}+ y[/itex]. Rewrite that as [itex]3\sqrt{1- y^2}= 2- y[/itex] and square both sides: [itex]9(1- y^2)= 4- 4y+ y^2[/itex] or [itex]9- 9y^2= 4- 4y+ y^2[/itex] so [itex]10y^2- 4y- 5= 0[/itex]. Solve that using the quadratic formula to find y= cos(X) and take the arcsine to find X.21385 said:
The process for solving for X in a trig equation involves using trigonometric identities and algebraic manipulations to isolate the variable, X, on one side of the equation. This typically requires using inverse trigonometric functions, such as arcsin, arccos, and arctan.
To determine which trig identities to use, you must first identify the type of trig equation you are dealing with. This can be done by looking at the given equation and seeing if it contains any trigonometric functions, such as sin, cos, or tan. Once you know the type of equation, you can then use the appropriate identities to manipulate the equation and solve for X.
Yes, there are a few special cases to be aware of when solving for X in a trig equation. These include equations with multiple angles, equations with fractions, and equations with multiple solutions. It is important to carefully consider these cases and use the appropriate techniques to solve for X.
Yes, a calculator can be a helpful tool when solving for X in a trig equation. However, it is important to remember that calculators may not always give exact solutions and may round off decimal values. It is also important to check your answer by plugging it back into the original equation to ensure it is correct.
One tip for solving for X in a trig equation more efficiently is to try to simplify the equation as much as possible before using any trig identities. This can help reduce the number of steps needed to solve for X. Additionally, it can be helpful to have a good understanding of basic trigonometric identities and how they can be used to manipulate equations.