# Solving trigonometric equations:

• Aug 12th 2011, 09:16 AM
glambeth
Solving trigonometric equations:
Solve https://kcdistancelearning.blackboar...es/sa033-1.jpg for https://kcdistancelearning.blackboar...es/sa033-2.jpg.

Here's my work:
sin(x) + sin(2x) = 0
___-
what do I do now? I can't think of any trig identities or anything to simplify it? Do i just do sin(x) = - sin(2x) which obviously isn't true, does anyone know??
• Aug 12th 2011, 09:24 AM
Ackbeet
Re: Solving trigonometric equations:
Your pictures are broken. Try using Imageshack or some free image hosting. Or you can also upload to MHF, now that pictures appear to be working again.
• Aug 12th 2011, 09:27 AM
glambeth
Re: Solving trigonometric equations:
Sorry about that, the picture is solve for sin(x) + 2*sin(x)*cos(x) = 0 for 0 degrees <= x < 180 degrees
I used a double angle idendtity to reduce from the aforementioned equation to sin(x) + sin(2x) = 0
• Aug 12th 2011, 09:38 AM
Plato
Re: Solving trigonometric equations:
Quote:

Originally Posted by glambeth
Sorry about that, the picture is solve for $\displaystyle \sin(x) + 2\sin(x)\cos(x) = 0$ for 0 degrees <= x < 180 degrees

Factor $\displaystyle \sin(x)[1+2\cos(x)]=0$ so
$\displaystyle \sin(x)=0~\text{ or }~\cos(x)=-\frac{1}{2}$.
• Aug 12th 2011, 09:56 AM
glambeth
Re: Solving trigonometric equations:
I see now, so x is equal to 0, 120, or 180?
• Aug 12th 2011, 10:13 AM
anonimnystefy
Re: Solving trigonometric equations:
since x is strictly less than 180 degrees you should not take that as the answer.
• Aug 12th 2011, 10:15 AM
glambeth
Re: Solving trigonometric equations:
Thanks, no idea how I missed that!