Find all solutions of sin on the interval

[nickb145]

Homework Statement

i have

solve 7sin(2x)-13sin(x)=0
for all solutions 0≤X<2p
I used the double angle formula for sin(2x)=2sin(x)cos(x)

The Attempt at a Solution

I'm getting stuck near the end
7(2sin(x)cos(x)-13sin(x))
14sin(x)cos(x)-13sin(x)

now I am stuck

 

[Curious3141]

Homework Statement

i have

solve 7sin(2x)-13sin(x)=0
for all solutions 0≤X<2p
I used the double angle formula for sin(2x)=2sin(x)cos(x)

The Attempt at a Solution

I'm getting stuck near the end
7(2sin(x)cos(x)-13sin(x))
14sin(x)cos(x)-13sin(x)

now I am stuck

What you wrote aren't equations. An equation must have two sides separated by an '='. In this case, your right hand side (RHS) equals 0.

In that final equation, can you find a common factor between the two terms?

 

[nickb145]

What you wrote aren't equations. An equation must have two sides separated by an '='. In this case, your right hand side (RHS) equals 0.

In that final equation, can you find a common factor between the two terms?

That is what i am trying ot figure out. I would just say sin(x) could be factored out.

the 14sin and the 13sin are just throwing me off.

 

[nickb145]

Yep that was it. found the solutions. it was sin(x) that was the common factor. sin(x)=0 and cos(x)=13/14

x= pi, 0 .3801 and 5.902