## anonymous 4 years ago I'm trying to solve this but I honestly have no idea how to move forward. All I have done so far is this: theta=tan^-1(-1) Now I'm stuck <_>

1. ash2326

@greysmither what's tan 45?

2. anonymous

it is 135 degree ,, Aren't u allowed to use calculator??

3. ash2326

Avva 135 is just one of the answer, it has several answers

4. amistre64

tan-1 only has one answer :)

5. ash2326

@amistre64 tan (theta)=-1 will have several solutions

6. amistre64

yep

7. anonymous

yup you can add 180 degrees and you'll figure out that 135 n 315 both have tan of -1

8. ash2326

$\tan \theta=-1$ so $\theta = n\pi +3\frac{\pi}{4}$ n=0, 1, 2, 3 and so on

9. anonymous

So this pretty much a unit circle-dependent problem?

10. anonymous

this is*

11. ash2326

Yeah:)

12. anonymous

Could it also be $7\pi/4 + \pi n$?

13. anonymous

since both of those quadrants create -1?

14. ash2326

Yeah it should be $n\pi \pm \pi/4$ n=1,2 ,3 and so on I missed that, it'd include $$7\pi/4 + n\pi$$ also

15. anonymous

I thought that you couldn't include pi/4 and 5pi/4 in quadrants 1 and 3 because they equal 1 when I'm looking for -1?

16. anonymous

So confusing :(

17. ash2326

Sorry, Just wait for some time, I'll help you:)

18. ash2326

Sorry kept you waiting:(

19. anonymous

Its okay I really appreciate your help

20. ash2326

We have $\tan x=-1$ so x is eithere 3pi/4 , 7pi/4 and so on $x= n\pi -\pi/4$ if n=1 x=3 pi/4 n=2 x= 7 pi/4 so this will include all possible solutions. This is your answer

21. anonymous

So, just to clarify $x=-\pi/4+n \pi$ is the final answer. I can't thank you enough!! I wish I could give you 100 medals ;)

22. ash2326

Thanks Greysmither , this is the answer:)