## anonymous one year ago Which value is a solution for the equation tan x/2=0 3pi/2 pi 2pi pi/2

1. mathstudent55

Where is the tangent equal to zero?

2. anonymous

I'm not sure?

3. mathstudent55

Think of the tangent as being $$\tan x = \dfrac{\sin x}{\cos x}$$ The tangent is zero where the sine is zero. At what values is the sine zero?

4. anonymous

would it also be zero?

5. mathstudent55

The function y = sin x is zero at all integer multiples pf pi. |dw:1437451807607:dw|

6. anonymous

meaning pi would be the answer, right?

7. mathstudent55

tan x = 0 at ... -pi, 0, pi, 2p-i, 3pi, ...

8. mathstudent55

So solving your equation, $$\tan \dfrac{x}{2} = 0$$ $$\dfrac{x}{2} = ... -\pi, 0, \pi, 2\pi, ...$$ $$x = ... -2\pi, 0, 2 \pi, 4 \pi, ...$$

9. anonymous

I'm sorry I'm still confused?

10. mathstudent55

Remember that your equation was not tan x = 0 Your equation was tan x/2 = 0 Once we found where the tangent has a value of zero, which is every integer multiple of pi, that means x/2 equals every integer multiple of pi. Now we need x. When you multiply every integer multiple of pi by 2, you get every even multiple of pi. The solution to the equation tan x/2 = 0 is every even multiple of pi. There is only one choice that is an even multiple of pi.

11. anonymous

2pi??

12. mathstudent55

Correct.

13. anonymous

Thanks!

14. mathstudent55

You're welcome.

15. anonymous

To start off, let's drop the x/2 and just say tanx. Where does tan x = 0?

16. anonymous

if you know where tanx = 0. I know your question is tan(x/2), but I was just seeing if you knew tanx = 0. So that means is if it were just X, x would = pi. But we have (x/2). So instead of x = pi, I'll say (x/2) = pi and then say solve for x :3

17. anonymous

18. mathstudent55

Isn't that exactly what I did above?

19. anonymous

ya but I wanted to check it im bored soo bored

20. UsukiDoll

there's nothing wrong with verification. As long as it's not spam, there's nothing bad about it.