An equation of the tangent line to the curve:
y= f(x) = x(9cosx - 3sinx)
at the point is y =
$\displaystyle f(x) = x(9\cos x - 3\sin x ) $
$\displaystyle f(3\pi) = 3\pi(9\cos (3\pi) - 3 \sin (3\pi) ) $
$\displaystyle f(3\pi) = 3\pi(-9) = -27\pi $
$\displaystyle f'(x) = (9\cos x - 3 \sin x ) + x ( 9(-\sin x ) - 3 \cos x ) $
$\displaystyle f'(x) = (9\cos x - 3 \sin x ) + x (-9\sin x - 3 \cos x ) $
$\displaystyle f'(3\pi) = (9\cos (3\pi) - 3 \sin (3\pi) ) + 3\pi (-9\sin (3\pi) - 3 \cos (3\pi) ) $
$\displaystyle f'(3\pi) = -9 + 9\pi $
$\displaystyle \frac{y-(-27\pi)}{x-3\pi} = -9 + 9\pi $
you can continue