Question

Helppppppppp !!!! Someone help me

Answer 1

`-(1)/(2)`

Explanation:

Given:

`\sin 30^(\circ)=(1)/(2)`

Find:
`\sin 210^(\circ)`

I method: Use formula

`\sin (\pi +\alpha)=-\sin \alpha`

Then

`210^(\circ)=180^(\circ)+30^(\circ)`

and

`\sin 210^(\circ)=\sin (180^(\circ)+30^(\circ))=-\sin 30^(\circ)=-(1)/(2)`

II method: Use formula

`\sin(\alpha +\beta)=\sin \alpha\cos \beta+\sin \beta\cos \alpha`

Then

`\sin 210^(\circ)=\sin (180^(\circ)+30^(\circ))\\ \\=\sin 180^(\circ)\cos 30^(\circ)+\sin 30^(\circ)\cos 180^(\circ)\\ \\=0\cdot \cos 30^(\circ)+\sin 30^(\circ)\cdot (-1)\\ \\=-\sin 30^(\circ)\\ \\=-(1)/(2)`