For the function f(x) = sin (arctan x), is sin the same as arctan X?

Answer 1

arctan x should be interpreted as "the angle whose tangent is x". So draw a right triangle and include an angle whose tangent is x. Then figure out the sine of that angle in terms of x and you're done.

Easiest way to do this is to let the side opposite the angle be x and the side adjacent to the angle be 1. Then the hypotenuse will have length sqrt(1+x^2).

Answer 2

The previous poster was wrong. The notation arctan x means the inverse function for tan x. In other words, it undoes the tangent.

Your function takes a number x, finds the angle whose tangent is x and then takes the sine of that angle. In other words, if tan(A)=x, what is sin(A)? If you draw a triangle showing the relation tan(A)=x, then you should be able to find sin(A) in terms of x. But you must use a pythagorean identity to do so.

Answer 3

No sin and arctan x is worlds apart.

Answer 4

well tan is equal to sin/cos so arctan or tan^(-1) is equal to cos/sin so sin is not equal to arctan

Answer 5

no, two totally different functions.