Question

I need help with an advanced trig equation picture included

Answer 1

Given:

`5\sin 2\alpha+6\sin \alpha=0,\: 0\le\alpha<\: 2\pi`

To find: the value of the angle

`\alpha`

Step-by-step explanation:

Solving the equation, we get

`\begin{gathered} 5\sin 2\alpha+6\sin \alpha=0 \\ 5\sin 2\alpha=-6\sin \alpha \end{gathered}`

Using the identity,

`\sin 2\alpha=2\sin \alpha\cos \alpha`

So, we write

`\begin{gathered} 5(2\sin \alpha\cos \alpha)=-6\sin \alpha \\ 5\cos \alpha=-3 \\ \cos \alpha=-(3)/(5) \\ \alpha=\cos ^(-1)(-(3)/(5)) \\ \alpha=2.214,4.069 \end{gathered}`

Final answer: The value of the angle is

`\alpha=2.214,4.0689`