Solving for x and y means finding the values of x and y that satisfy the given equation. In other words, we are trying to find the specific values of x and y that make the equation true.
The equations sin-1x=y and siny=x are inverse functions. This means that when one equation is true, the other equation is also true. In other words, the two equations are essentially saying the same thing in a different way.
To solve for x and y, we need to use algebraic techniques such as substitution or elimination. In the equations sin-1x=y and siny=x, we can substitute sin-1x for y in the second equation to get sin-1x=x. This can then be solved using trigonometric identities or a graphing calculator.
Sin-1x is the inverse function of sine, while sinx is the original sine function. Sin-1x takes in a value for the output of sine and gives the corresponding input value, while sinx takes in an input value and gives the corresponding output value. In other words, sin-1x "undoes" the effect of sinx.
Solving for x and y allows us to find specific solutions to the equations and understand the relationship between the trigonometric functions involved. It also helps us to solve more complex problems that involve these equations, such as finding missing angles or sides in a right triangle.