Question

How do you solve `sin^2x-7sinx=0`?

Answer 1

`x=0+kpi`

Explanation:

`"take out a "color(blue)"common factor of "sinx`

`rArrsinx(sinx-7)=0`

`"equate each factor to zero and solve for x"`

`sinx=0rArrx=0+kpitok inZZ`

`sinx-7=0rArrsinx=7larrcolor(blue)"no solution"`

`"since "-1<=sinx<=1`

`"the solution is therefore "x=0+kpitok inZZ`

Answer 2

General solution:
`x = kpi`, k belongs to integers

Explanation:

`sin^2x-7sinx=0`

Factor:
`sinx(sinx-7)=0`

therefore:
1: `sinx = 0` and 2: `sinx-7=0`

2 can be simplified to `sinx=7`
therefore since `sinx=7` has no solutions, look at `sinx=0`

So when is `sinx=0`?

the general solution is:
`x = kpi`, k belongs to integers

however if they give certain parameters such as `0 < x < 2pi`,
then for this case the answer will be:

`x={0, pi}`

Answer 3

`x=0, pi or 2pi`
Or, in degrees, `x=0, 180^o or 360^o`

Explanation:

First factor the equation:
`sin^2x-7sinx=0`
`sinx(sinx-7)=0`

Then apply the Zero Product Rule, where if a product equals zero, then one or more of the factors must equal zero.

`sinx = 0 or sinx-7 = 0`

Solving, by isolating `sinx`,

`sinx=0 or sinx=7`

There are no values of `x` that will satisfy `sinx=7` since the domain of `sinx` is `-1<=x<=1`.

For `0<=x<=2pi` the values of x that satisfy `sinx=0` are `x=0, pi or 2pi`
In degree measure, for `0<=x<=360^o` the values of `x` that satisfy `sinx=0` are `x=0, 180^o or 360^o`