[Math] Find where the tangent line passes through the origin.

Question

I need help finding where the tangent line of $f(x) = 5 \cos(3x)$ passes through the origin.
I know the equation of a tangent line is $y = f'(a)(x – a) + f(a)$.
So I my first thought was to set y and x equal to zero, then solve for a. Is this correct? If so can you help me solve for a, because I got stuck.

Answer 1

First calculate the points where the tangent line goes through $(0,0)$; you just have to solve $f(x)/x=f'(x)$. In our case, any number $x$ satisfying $-3x\tan(3x)=1$ is the first coordinate of such a point.