- #1
gymko
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Homework Statement
I have a problem, I don't know to substantiate, why arcsin(sin(x)) = sin(arcsin(x)) = x ?
Thank you very much for each advice.
Did you mean all x in [-1,1]? (Or are you making an assertion about the complex Arcsin function?)g_edgar said:[itex]\sin(\arcsin(x)) = x[/itex] for all real [itex]x[/itex]
Gregg said:y=arcsin(sin(x))
sin(y) = sin(x)
y = x
Hurkyl said:Did you mean all x in [-1,1]? (Or are you making an assertion about the complex Arcsin function?)
Hurkyl said:
gymko said:My question is: why arcsin(sin(x)) is possible to regulate for x. Why arcsin(sin(x)) = x?
Why graph for y = arcsin(sin(x)) is y = x?
Thank you.
The inverse of a function is a mathematical operation that undoes the original function. It essentially reverses the process of the original function.
The inverse of sin is arcsin, also known as inverse sine or sin-1. It is the inverse function of sin, and is used to solve for the angle when given the sine value of that angle.
To show that arcsin is the inverse of sin, we must prove that the composition of the two functions, sin(arcsin(x)) and arcsin(sin(x)), results in the identity function f(x) = x. This can be done algebraically or graphically.
The domain of sin is all real numbers, while the range is between -1 and 1. The domain of arcsin is also all real numbers, but the range is between -π/2 and π/2.
Inverse functions are important because they allow us to solve for unknown values in equations and to perform operations that would otherwise be impossible. Inverse functions are also used in various areas of mathematics and science, such as trigonometry, calculus, and physics.