Fourier transformation with two signals

Question

So I have two signals
$$m(t) = 336\cdot\rm{sinc}(24t)$$ $$x(t) = m(t)\cos(400\pi t)$$ How do I calculate fourier transformation for $x(t)$?
I already calculated:
$$M(f) = 14\cdot\rm{rect}(\frac{f}{24})$$ and fourier transformation for $\cos(400 \pi t)$, lets just call this $y(t)$
$$Y(f) = \frac{1}{2}(\delta(f - 200) + \delta(f + 200))$$ $$X(f) = 14\rm{rect}(\frac{f}{24}) \cdot \frac{1}{2}(\delta(f - 200) + \delta(f + 200))$$ which is wrong answer. What am I doing wrong?

Answer 1

Look up the convolution theorem for the Fourier Transform

$$\begin{align*}X(f)&=\mathscr{F}\left\{x(t)\right\}\\ \\ &= \mathscr{F}\left\{m(t)\cdot y(t)\right\}\\ \\ &=\mathscr{F}\left\{m(t)\right\}*\mathscr{F}\left\{ y(t)\right\}\\ \\ X(f) &= M(f) * Y(f)\\ \end{align*}$$

Where '$\cdot$' denotes multiplication and '$*$' denotes convolution. Your answer just appears to have multiplication, given your notation.