cos(arcsin(2/x))?

Question

in radians

Answer 1

You know that the sine of the angle is 2/x. By using the pythagorean theorem (and by drawing a triangle), you find the adjacent side of the triangle to be sqrt(x^2 - 4).

The hypotenuse is x, so...

cos(arcsin(2/x)) = sqrt(x^2 - 4)/x radians = (x+2)(x-2)/x radians

Sorry, but you just can't get a nice, clean answer like pi/4, since x is still unknown.

Answer 2

you are looking for the cosinus of an angle whose sinus is 2/x
you know that sinus and cosinus are related b
sin^2+cos^2 = 1
so cos(arc sin(2/x) =+-sqrt(1-4/x^2)
You can´t define +- even if you know x ,as for every value of the sinus of an angle (except 1 and-1) there are two different angles