Question

Please help me :(( I need the answer :(

Answer 1

`\theta = 60^\circ \;and\; \theta = 300^\circ`

Explanation:

Given

`\sin \left(2\theta\right)=\sin \left(\theta\right)`

Use the identity:
`\sin(2\theta) = 2 \sin(\theta)\cos(\theta)`

=>
`2 \sin(\theta)\cos(\theta) = \sin(\theta)`

Divide both sides by
`\sin(\theta)`

=>
`2 \cos(\theta) = 1`

`= > \cos(\theta) = (1)/(2)`

`= > \,\theta=\cos^(-1)\left((1)/(2)\right)`

`\cos^(-1)\left((1)/(2)\right) \;is\: (\pi)/(3)} \text{ in the first quadrant and $(5\pi)/(3)$ in the fourth quadrant}}`

In degrees this corresponds to

`(\pi)/(3) = (\pi)/(3) * (180^\circ)/(\pi) = 60^\circ\\\\and\\\\(5\pi)/(3) = (5\pi)/(3) * (180^\circ)/(\pi) = 300^\circ\\`

Answer

`\theta = 60^\circ \;and\; \theta = 300^\circ`