$$\lim_{t \to 0^-} \sin{\left(t \right)} = 0$$ More at t→0 from the left $$\lim_{t \to 0^+} \sin{\left(t \right)} = 0$$ $$\lim_{t \to \infty} \sin{\left(t \right)} = \left\langle -1, 1\right\rangle$$ More at t→oo $$\lim_{t \to 1^-} \sin{\left(t \right)} = \sin{\left(1 \right)}$$ More at t→1 from the left $$\lim_{t \to 1^+} \sin{\left(t \right)} = \sin{\left(1 \right)}$$ More at t→1 from the right $$\lim_{t \to -\infty} \sin{\left(t \right)} = \left\langle -1, 1\right\rangle$$ More at t→-oo