Sin Cos Worded Problem

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Stuck at part B.

When I directly substitute (3x) for (x) and let f(x)=8/9(root 6) I get the correct answer which is pi/36.

But arent you supposed to let 3x=z and then sub (z/3) for x into the equation?

I'm a bit confused at when to use direct substitution... can someone explain.

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If you let $z=3x$, then you're computing $T(z)$ which means you substitute $z$ for $x$ in the expression, not $\frac{z}{3}$.