Grade 12 Math - Trigonometry Question.

[lily.123]

Homework Statement

tanxsinx+sinx=0
0≤x≤2∏

What is the largest domain given?

Problem.

I'm not sure what to do with this question. It's probably pretty simple, but I'm absolutely rubbish at math. Hopefully someone can help me with this? Thanks.
-Lily

 

[Bohrok]

Try factoring out a sin from the left side, and use the zero product property to solve.

 

[Vorde]

Well it's asking you in the domain 0 to 2pi when is that equation zero. So the first think I would do is pull a sin(x) out of the left hand and then you can split the equation up in two things, with the correct solutions being when either one is zero.

 

[lily.123]

So, I'm assuming this?


tanxsinx+sinx=0
sinx(tanx + 1) = 0
sinx = 0
x = pi
tanx = -1
x = 3pi/4 , 7pi/4

 

[Mentallic]

So, I'm assuming this?


tanxsinx+sinx=0
sinx(tanx + 1) = 0
sinx = 0
x = pi
tanx = -1
x = 3pi/4 , 7pi/4

Yes, but for $\sin(x)=0$ there are more values of x where this is satisfied.

 

[lily.123]

I'm not quite sure I follow?

 

[Mentallic]

Remember the domain is $0\leq x \leq 2\pi$. So where is $\sin(x)=0$ in this domain? Surely more places than just at $x=\pi$. Take x=0 for example.

 

[lily.123]

Oh, I get it! Thanks everyone!