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

3 Answers
Mar 6, 2018

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

Mar 6, 2018

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}

Mar 6, 2018

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