Grade 12 Math - Trigonometry Question.

lily.123

1. The problem statement, all variables and given/known data

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

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

lily.123

I'm not quite sure I follow?

Mentallic

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

lily.123

Oh, I get it! Thanks everyone!