## anonymous one year ago Thanks for helping! I was given a pre calc problem which I simplified to: (tanx-2)(tanx-1)=0 The question asks me to solve from there. However, it doesn't ask me to solve in terms of 0 to 2pi, it asks for all solutions. I know that I have to add an extension once I find the final solution, but am having a hard time figuring out how to do so. I know it looks something like+n*pi*k or something like that. Thank You!

1. anonymous

@Kainui @jim_thompson5910 @amistre64 @ganeshie8 @zepdrix @campbell_st @Loser66

2. anonymous

@Luigi0210 @robtobey @sammixboo @Zarkon @pooja195 @radar

3. zepdrix

Hmm the 2 is going to cause a bit of a problem :) Not a nice friendly angle there. But the 1 is ok.

4. anonymous

I think the one is pi/4?

5. zepdrix

Applying our Zero-Factor Property,$\Large\rm \tan x-1=0$Add 1 to each side,$\Large\rm \tan x=1$ Ok good, yes this corresponds to pi/4 in the first quadrant.

6. anonymous

since it is for all solutions, should I add the extension? Or is there another thing I need to do?

7. zepdrix

$\Large\rm x=\frac{\pi}{4}+k \pi, \quad k=0,\pm1,\pm2,...$Tangent is a little different than sine and cosine. It is period in pi not in 2pi. So we want to allow multiples of pi to be added on and give us the same value through tangent.

8. zepdrix

periodic* blah

9. anonymous

So I'd just say pi/4+kpi and add nEz to the right?

10. zepdrix

$$\Large\rm k\in\mathbb{Z}$$ ya that works out nicely I guess :)

11. anonymous

cool and I don't need to add 5pi/4+kpi? As it is another solution

12. zepdrix

5pi/4 = pi/4 + 1*pi so it's already included in our set of solutions with the k

13. zepdrix

we just need to deal with this ugly tanx-2 now :d

14. anonymous

lol, I simplified it to 7pi/20

15. anonymous

I think that sounds right, but am not sure

16. zepdrix

Woah I'm not really sure 0_O I was just going to be lazy and call the angle $$\Large\rm \arctan(2)$$

17. anonymous

I asked my teacher, but he said I needed to go further

18. zepdrix

mmm ok thinking :)

19. anonymous

cool

20. anonymous

I found the radian in decimals and divided by pi and converted that into a fraction

21. anonymous

If that is the correct process

22. anonymous

and multiplied pi of course :)

23. zepdrix

arctan(2) = 1.1071487... divide by pi gives: $$\Large\rm 0.352416382\pi$$ then what did you do? 0_o how did you convert to fraction?

24. anonymous

yea

25. anonymous

26. anonymous

is that right? I'm not too good at this ha ha

27. anonymous

I converted with some calculator

28. anonymous

which gave me 7/20, which is about right

29. anonymous

I rounded it for the calc

30. zepdrix

im not sure how to get an exact answer :d its look like it's some irrational multiple of pi, like some weird square root maybe. so ya approximating is probably the right way to go. I would leave it as a decimal though maybe. $\Large\rm x=0.352\pi+k \pi$$\Large\rm x=(0.352+k)\pi,\qquad k\in\mathbb{Z}$

31. zepdrix

Maybe you guys have some fun technique for finding arctan(2), maybe my brain is a lil rusty hehe

32. anonymous

thanks for the help! I'll give you a medal

33. zepdrix

np c:

34. anonymous

:)