To solve for x in an equation like sin x = 2/pi, you need to use inverse trigonometric functions. In this case, you would use the inverse sine function (sin^-1) to isolate x on one side of the equation. This will give you the value of x in radians.
No, this equation cannot be solved algebraically. Trigonometric equations like sin x = 2/pi require the use of inverse trigonometric functions to solve for x.
The solution to sin x = 2/pi is x = sin^-1(2/pi), which is approximately 0.6435 radians or 36.87 degrees.
Yes, there are an infinite number of solutions to this equation. In addition to the principal solution, which is x = sin^-1(2/pi), there are infinitely many other solutions that can be found by adding or subtracting multiples of 2π to the principal solution.
You can check your solution by substituting the value of x into the original equation and seeing if it satisfies the equation. In this case, you can substitute 0.6435 radians or 36.87 degrees into sin x = 2/pi and see if the equation holds true.