Write the expression in algebraic form. [hint: sketch a right triangle.] tan (arcsec (x/3))

Sketch a right triangle having adjacent side (A) is given as "3", hypotenuse side (H) is "x" and assigning angle "a" as the angle between A and H. Using Pythagorean theorem, you will get "square root of x-squared minus 9" as the opposite side (O). Using SOH CAH TOA function, and since secant is the reciprocal of cosine, sec (a) = x/3. Thus, a = arcsec (x/3). The remaining expression tan (a) is Opposite side over Adjacent side which is equal to "square root of x^2 - 9" over "3". Therefore, the algebraic expression would be: tan (arcsec (x/3)) = "sqrt (x^2 - 9) " / 3. Different answers can be made depending on which side you consider the "3" and "x".