`1.`
`a.`

`30^0=``\pi/6(rad)`

`80^0 30’=``(80+30/60)^0=(80+1/2)^0=((160+1)/2)^0=(161/2)^0``=>` `(161/2)^0=161/2.\pi/180=(161\pi)/360(rad)`

`b.`

`(5\pi)/8=(5.180^0)/8=900^0/8=112,5^0`

`3,75=3,75.(180^0)/\pi=675^0/\pi`

`2.`

\begin{align*} \text{Ta có: a. } \quad \cos\left( \frac{4\pi}{3} \right) &= \cos\left( \pi + \frac{\pi}{3} \right) = -\cos\left( \frac{\pi}{3} \right) = -\frac{1}{2} \\ \sin\left( \frac{4\pi}{3} \right) &= \sin\left( \pi + \frac{\pi}{3} \right) = -\sin\left( \frac{\pi}{3} \right) = -\frac{\sqrt{3}}{2} \\ \Rightarrow N\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right) \end{align*}

\begin{align*} \text{b.} \quad \tan\left( \frac{4\pi}{3} \right) &= \frac{\sin\left( \frac{4\pi}{3} \right)}{\cos\left( \frac{4\pi}{3} \right)} = \sqrt{3} \\ \cot\left( \frac{4\pi}{3} \right) &= \frac{1}{\tan\left( \frac{4\pi}{3} \right)} = \frac{\sqrt{3}}{3} \end{align*}