Write an algebraic expression for y=tan (cos^-1 x/3)for 0<x<3.

Question

Please Help!!

Answer 1

look at the cos^-1 (x/3)
construct a triangle with base of x and hypotenuse of 3
by Pythagoras:
r^2 = x^2 + y^2
3^2 = x^2 + y^2
y^2 = 9 - x^2
y = √(9-x^2)

so we want the tangent
tan (cos^-1 x/3)
= opposite/adjacent
= √(9-x^2)/3