1. On a: $$z_1=\cos(\theta)-i\sin(\theta)=\overline{e^{i\theta}}=e^{-i\theta}$$ Donc: $$~~\boxed{~~\arg z_1=-\theta~~}$$
  2. On a: \begin{align*} z_2&=-\cos(\theta) - i\sin(\theta)\\ z_2&=-e^{i\theta}\\ z_2&=e^{i\pi}e^{i\theta}\\ z_2&=e^{i(\pi+\theta)} \end{align*} Donc: $$\boxed{~~\arg z_2=\pi+\theta~~}$$
  3. On a: \begin{align*} z_3&=-\cos \theta +i \sin \theta\\ z_3&=\cos(\pi-\theta)+i\sin(\pi-\theta)\\ z_3&=e^{i(\pi-\theta)}\\ \end{align*} Donc: $$\boxed{~~\arg z_2=\pi-\theta~~}$$
  4. On a: \begin{align*} z_4&=\sin \theta - i\cos \theta\\ z_4& =-i(\cos\theta+i\sin\theta)\\ z_4&=-ie^{i\theta}\\ z_4&=e^{i\frac{3\pi}{2}}e^{i\theta}\\ z_4&=e^{i(\frac{3\pi}{2}+\theta)} \end{align*} Donc: $$\boxed{~~\arg z_4=\dfrac{3\pi}{2}+\theta~~}$$