Question

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!

Answer 1

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

Answer 2

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

Answer 3

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

But the 1 is ok.

Answer 4

I think the one is pi/4?

Answer 5

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.

Answer 6

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

Answer 7

\[\Large\rm x=\frac{\pi}{4}+k \pi, \quad k=0,\pm1,\pm2,...\]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.

Answer 8

periodic* blah

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

5pi/4 = pi/4 + 1*pi

so it's already included in our set of solutions with the k

Answer 13

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

Answer 14

lol, I simplified it to 7pi/20

Answer 15

I think that sounds right, but am not sure

Answer 16

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

Answer 17

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

Answer 18

mmm ok thinking :)

Answer 19

cool

Answer 20

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

Answer 21

If that is the correct process

Answer 22

and multiplied pi of course :)

Answer 23

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?

Answer 24

yea

Answer 25

about 7/20

Answer 26

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

Answer 27

I converted with some calculator

Answer 28

which gave me 7/20, which is about right

Answer 29

I rounded it for the calc

Answer 30

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.

\[\Large\rm x=0.352\pi+k \pi\]\[\Large\rm x=(0.352+k)\pi,\qquad k\in\mathbb{Z}\]

Answer 31

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

Answer 32

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

Answer 33

np c:

Answer 34

:)