Đáp án: `P=-\frac{4+3\sqrt{3}}{10}`
Giải:
Ta có:
`sin\alpha=sin(π-\alpha)=-\frac{3}{5}`
`sin^2\alpha+cos^2\alpha=1`
⇔ `cos^2\alpha=1-sin^2\alpha=1-(-\frac{3}{5})^2=\frac{16}{25}`
⇔ `cos\alpha=-\frac{4}{5} \ (π<\alpha<\frac{3π}{2})`
`P=sin(\alpha+\frac{π}{6})`
`P=sin\alpha.cos\frac{π}{6}+cos\alpha.sin\frac{π}{6}`
`P=-\frac{3}{5}.\frac{\sqrt{3}}{2}-\frac{4}{5}.\frac{1}{2}`
`P=-\frac{4+3\sqrt{3}}{10}`
