Solve the given equation
tan^2(theta)-2sec(theta)=2

- Babynini

Solve the given equation
tan^2(theta)-2sec(theta)=2

- katieb

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- Babynini

@freckles I love you <3 just so you know xD
I've gotten to
sec(theta)=-1/2 and sec(theta)=1

- Babynini

But on the unit circle secant never = -1/2 and it equals 1 at 0

- Babynini

@peachpi :)?

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## More answers

- anonymous

Pi and -pi work, but they're certainly not the only answers. Positive and negative 1.231, 5.052, and 7.514 work as well.

- Babynini

how did you get those?

- Babynini

does pi(n) where n is an interger work?

- anonymous

tan² x -2 sec x = 2
sec² x - 1 -2 sec x = 2
sec²x - 2 sec x - 3 = 0
(sec x - 3)(sec x + 1) = 0
sec x = 3, sec x = -1

- Babynini

ooh crud. I added two instead of subtracting it

- Babynini

oh wow I messed up all over the place.

- Babynini

what did you do with the 2secx?

- Babynini

oh I see
2secx-sec^2x-2 = 0

- anonymous

I factored. and you have them reversed in the equation you just wrote

- Babynini

What's the correct way?

- anonymous

sec²x - 2 sec x - 3 = 0

- Babynini

ah right. so but secant never = 3 on the unit circle..

- Babynini

and = -1 and pi

- anonymous

yes, pi is a solution. For sec x = 3, the solution is x = arcsec 3

- Babynini

ah k. So for me with my little scientific calculator how do I do arc sec 3

- Babynini

sec = 1/cos
but with the inverse I want to be careful o.o

- anonymous

sec x = 3
cos x = 1/3
x = arccos (1/3)

- Babynini

oh! :)

- anonymous

that'll give you an angle in the 1st quadrant. Subtract it from 360 to get the angle in the 4th quadrant.

- anonymous

or rather 2pi

- Babynini

does it work to add two pi to that? or just subtracting it from 2pi?

- Babynini

the answers they give are
kpi = we have this one!
0.72+2kpi = we don't have this.
5.56+2kpi = and we dont' have this either.

- anonymous

adding 2pi just gives the same angle you already found. Subtracting x from 2pi gives the angle in the 4th quad.
Where did these answers come from?

- Babynini

aah I see
the answer part of the book
I'm doing the odd problems in my textbook which gives the answers in the back.

- Babynini

oh crap. Just a moment.

- anonymous

I'm getting 5.05 and 1.23

- Babynini

Sorry, yeah. I was looking at 7 instead of 5.
the answers are
(2k+1)pi, 1.23+2kpi, 5.05+2kpi

- anonymous

ok. you know how to get those?

- Babynini

um
1.23, 5.05 came from theta = arcos(1/3)
and pi came from sec(theta)=-1

- Babynini

and I understand the adding 2pi(k)

- Babynini

I'm not sure why the pi one is written as
(2k+1)pi ?

- anonymous

That's the same as π+2πk. They factored the pi out

- Babynini

ah ok I see.

- Babynini

haha I told myself I would keep doing these until I get the answer entirely on my own..but going like this it seems that won't be anytime soon =.=
K, this one makes sense now though :)

- anonymous

ok great. Maybe take a break if you don't have a deadline. These definitely take time to get used to

- Babynini

Final on Friday..hah but I may move onto studying another part.

- anonymous

ah.. I don't envy you. good luck

- Babynini

yeah xD thanks.

- Babynini

Precalc 2 man. phew.

- Babynini

For you it's probably no biggy xP

- anonymous

yeah give it a few years, you'll either never use it, or wonder how you lived without knowing it. There's no in-between

- Babynini

I fear it may be the latter D: Just because i despise it so much, i'm bound to end up being a math major lol

- Babynini

Welp, moving onto question next. Thanks for all your help :)

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