Question

Please help and explain this question!

Answer 1

2

Explanation:

Consider two functions:

`y=\sin x` and
`y=\sin 2x`

The period of each function is

`2\pi` and
`\pi`

This means that the graph of the function
`y=\sin x` (red graph) intersects by the horizontal line
`y=(1)/(2)` twice and the graph of the function
`y=\sin 2x` intersects by the horizontal line
`y=(1)/(2)` four times (blue graph) for
`x\in [0,2\pi ).`

So the equation
`\sin \theta=(1)/(2)` has 2 solutions and the equation
`\sin 2\theta=(1)/(2)` has 4 solutions. Thus, the difference is 2.