Babynini
  • Babynini
Solve the given equation tan^2(theta)-2sec(theta)=2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Babynini
  • Babynini
@freckles I love you <3 just so you know xD I've gotten to sec(theta)=-1/2 and sec(theta)=1
Babynini
  • Babynini
But on the unit circle secant never = -1/2 and it equals 1 at 0
Babynini
  • Babynini
@peachpi :)?

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More answers

anonymous
  • 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
  • Babynini
how did you get those?
Babynini
  • Babynini
does pi(n) where n is an interger work?
anonymous
  • 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
  • Babynini
ooh crud. I added two instead of subtracting it
Babynini
  • Babynini
oh wow I messed up all over the place.
Babynini
  • Babynini
what did you do with the 2secx?
Babynini
  • Babynini
oh I see 2secx-sec^2x-2 = 0
anonymous
  • anonymous
I factored. and you have them reversed in the equation you just wrote
Babynini
  • Babynini
What's the correct way?
anonymous
  • anonymous
sec²x - 2 sec x - 3 = 0
Babynini
  • Babynini
ah right. so but secant never = 3 on the unit circle..
Babynini
  • Babynini
and = -1 and pi
anonymous
  • anonymous
yes, pi is a solution. For sec x = 3, the solution is x = arcsec 3
Babynini
  • Babynini
ah k. So for me with my little scientific calculator how do I do arc sec 3
Babynini
  • Babynini
sec = 1/cos but with the inverse I want to be careful o.o
anonymous
  • anonymous
sec x = 3 cos x = 1/3 x = arccos (1/3)
Babynini
  • Babynini
oh! :)
anonymous
  • anonymous
that'll give you an angle in the 1st quadrant. Subtract it from 360 to get the angle in the 4th quadrant.
anonymous
  • anonymous
or rather 2pi
Babynini
  • Babynini
does it work to add two pi to that? or just subtracting it from 2pi?
Babynini
  • 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
  • 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
  • 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
  • Babynini
oh crap. Just a moment.
anonymous
  • anonymous
I'm getting 5.05 and 1.23
Babynini
  • Babynini
Sorry, yeah. I was looking at 7 instead of 5. the answers are (2k+1)pi, 1.23+2kpi, 5.05+2kpi
anonymous
  • anonymous
ok. you know how to get those?
Babynini
  • Babynini
um 1.23, 5.05 came from theta = arcos(1/3) and pi came from sec(theta)=-1
Babynini
  • Babynini
and I understand the adding 2pi(k)
Babynini
  • Babynini
I'm not sure why the pi one is written as (2k+1)pi ?
anonymous
  • anonymous
That's the same as π+2πk. They factored the pi out
Babynini
  • Babynini
ah ok I see.
Babynini
  • 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
  • anonymous
ok great. Maybe take a break if you don't have a deadline. These definitely take time to get used to
Babynini
  • Babynini
Final on Friday..hah but I may move onto studying another part.
anonymous
  • anonymous
ah.. I don't envy you. good luck
Babynini
  • Babynini
yeah xD thanks.
Babynini
  • Babynini
Precalc 2 man. phew.
Babynini
  • Babynini
For you it's probably no biggy xP
anonymous
  • 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
  • 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
  • Babynini
Welp, moving onto question next. Thanks for all your help :)

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