The problem specifies the point $(t_1,y_1)=\left(\pi,f(\pi)\right)$ where $f(t)=3\sin(2t)+5$ and $y=f(t)$. The equation of a tangent line is given by
You need to find $f(\pi)$ and $m=f'(\pi)$ and then substitute them into $(1)$.
Step 1: Find the derivative of $f$ at $\pi$.
Step 2: Find $f(\pi)$.
Therefore, the point is $(t_1,y_1)=(\pi,5)$ and the slope of the tangent line is $m=f'(\pi)=6$. Substitute these values into $(1)$ to find the equation of the tangent line.