Convolution, g(t)=sin(t)

Question

I have two functions:

$f(t)=(t+\pi)\theta(t+\pi)-2t\theta(t)+(t+\pi)\theta(t-\pi)$, (looks like $-|x|+1, -\pi < x < \pi$ )

and

$g(t) = \sin{(t)}$

Could someone please point me in the right direction of how to solve the convolution of $f(t)*g(t)$ ?

Thanks

Answer 1

$$f*g=\int_{-\pi}^{\pi} \sin(t-t')f(t')dt'=\int_{-\pi}^0 \sin(t-t')(t'+\pi)dt'+\int_0^{\pi} \sin(t-t')(\pi-t')dt'$$

And I'll presume that you can finish the integrals.