Help me solve this please!

Question

steve816 · Answer

$$\sin(2 \theta) + 1 = 0$$
So far, using the double angle formula, I have this.
$$2\sin \theta \cos \theta + 1 = 0$$

nerdsarecool · Answer

Dude

mathmale · Answer

Good start, Steve!
Trouble is, you now have two trig functions to worry about:  sine and cosine.
That double angle formula can be really useful.  But not here.
So, my question for you is:  Is there (or are there) another identity (identities) that would be more helpful here?

mathmale · Answer

$$\sin(2 \theta) + 1 = 0$$

steve816 · Answer

Not sure what to do...

mathmale · Answer

Could be solved for sin (2 theta).
Next, you could temporarily substitute x for 2 theta, obtaining 

$$\sin x=-1$$

mathmale · Answer

Can y ou solve this for x?  Hint:  there are an infinite number of solutions.

mathmale · Answer

take any one of these solutions and set it equal to 2 theta.

Then solve for theta.  

Again, the number of solutions is infiniite.  How would you indicate that in your answer?

steve816 · Answer

This is what I got$$\frac{ 3\pi }{ 2 } + 2\pi k$$

mathmale · Answer

How would you check that?  First, determine whether 3pi/2 is a solution.
Then, check out 3pi/2+2pi.
And so on.
Best never to consider a problem of this kind solved until you've checked your answer.

steve816 · Answer

I think I got it, thanks.