Rewrite sintan−1w−36w2 as an algebraic expression in w.=sintan−1w−36w2

The given expression is already an algebraic expression in w. However, if you want to simplify it, it's a bit tricky because it involves trigonometric and inverse trigonometric functions.

The expression is sin(tan^-1(w)) - 36w^2.

The sin(tan^-1(w)) part can be simplified using the Pythagorean identity sin^2(x) + cos^2(x) = 1.

If we let x = tan^-1(w), then tan(x) = w.

We can draw a right triangle with opposite side w, adjacent side 1 (since tan(x) = opposite/adjacent), and hypotenuse sqrt(w^2 + 1) (by the Pythagorean theorem).

Then sin(x) = opposite/hypotenuse = w/sqrt(w^2 + 1).

So sin(tan^-1(w)) = w/sqrt(w^2 + 1).

Therefore, the original expression can be rewritten as w/sqrt(w^2 + 1) - 36w^2.