find all values of x such that sin(sin(x))=1
To find all values of x such that sin(sin(x)) = 1, we need to solve the equation.
First, let's consider the equation sin(sin(x)) = 1.
To solve this equation, we need to take the inverse sine function (also called arcsin or sin^(-1)) of both sides of the equation. This will help us isolate the sin(x) term.
Applying the arcsin function to both sides, we get:
arcsin(sin(sin(x))) = arcsin(1).
The arcsin(sin(x)) term helps to find the values of x such that sin(x) = the given value.
Since the range of the arcsin function is -π/2 to π/2 (or -90 degrees to 90 degrees), the solution we obtain will lie within this range.
Now, the equation becomes:
sin(x) = 1.
In this case, the solution set is obtained by finding all x values such that sin(x) equals 1. This happens when x is an integer multiple of π plus π/2, i.e., x = (nπ + π/2), where n is an integer.
Therefore, all the values of x that satisfy the equation sin(sin(x)) = 1 are x = (nπ + π/2), where n is an integer.